# Khan/khan-exercises

fix exercises for deployment

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1 parent f91220c commit d6a5fb60de51f47a8395ae569e5c9e2543498aec jeffdyer committed Jan 27, 2012
115 exercises/factoring_diff_of_squares_polynomials_1.html
 @@ -1,72 +1,77 @@ - - Factoring Difference of Two Squares, Polynomials with A = 1 - + + Factoring Difference of Two Squares, Polynomials with A = 1 + -
-
+
+
- MathModel.init() - randRange(2, 9) - 1 - 0 - -b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("(x+"+b+")(x-"+b+")") + MathModel.init() + randRange(2, 9) + 1 + 0 + -b*b + MATH.polynomial([A, B, C], "x") + + MATH.parse("(x+"+b+")(x-"+b+")")
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

+

+ Factor the following expression: +

+

+ MATH.format(PROBLEM, "large") +

+
-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(x+2)(x-2)
+
+ Enter the factored expression here:
+ +
+
jQuery( "div.instruction input" ).val()
+
+ return MATH.isEqual(MATH.parse(guess), SOLUTION) +
+
+
+
+ jQuery( "div.instruction input" ).val( guess ) +
+
(x+2)(x-2)
+
-

- Recognize that the expression is of the form - MATH.format("a^2-b^2", "normalsize", KhanUtil.BLUE) - , which can be factored as - MATH.format("(a+b)(a-b)", "normalsize", KhanUtil.BLUE). -

-

- First, determine the values of - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+"x", "normalsize", KhanUtil.BLUE)

- MATH.format("b=\\sqrt{"+b*b+"}="+b, "normalsize", KhanUtil.BLUE) -

-

- Replace - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. -

-

- MATH.format("(x+"+b+")(x-"+b+")", "large", KhanUtil.ORANGE) -

+

+ Recognize that the expression is of the form + MATH.format("a^2-b^2", "normalsize", KhanUtil.BLUE) + , which can be factored as + MATH.format("(a+b)(a-b)", "normalsize", KhanUtil.BLUE). +

+

+ First, determine the values of + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a="+"x", "normalsize", KhanUtil.BLUE)

+ MATH.format("b=\\sqrt{"+b*b+"}="+b, "normalsize", KhanUtil.BLUE) +

+

+ Replace + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. +

+

+ MATH.format("(x+"+b+")(x-"+b+")", "large", KhanUtil.ORANGE) +

+
+
-
-
117 exercises/factoring_diff_of_squares_polynomials_2.html
 @@ -1,73 +1,78 @@ - - Factoring Difference of Two Squares, Polynomials with A != 1 - + + Factoring Difference of Two Squares, Polynomials with A != 1 + -
-
+
+
- MathModel.init() - randRange(2, 9) - randRange(1, 9) - a*a - 0 - -b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("("+a+"x+"+b+")("+a+"x-"+b+")") + MathModel.init() + randRange(2, 9) + randRange(1, 9) + a*a + 0 + -b*b + MATH.polynomial([A, B, C], "x") + + MATH.parse("("+a+"x+"+b+")("+a+"x-"+b+")")
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

+

+ Factor the following expression: +

+

+ MATH.format(PROBLEM, "large") +

+
-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(2x+3)^2
+
+ Enter the factored expression here:
+ +
+
jQuery( "div.instruction input" ).val()
+
+ return MATH.isEqual(MATH.parse(guess), SOLUTION) +
+
+
+
+ jQuery( "div.instruction input" ).val( guess ) +
+
(3x+2)(3x-2)
+
-

- Recognize that the expression is of the form - MATH.format("a^2-b^2", "normalsize", KhanUtil.BLUE) - , which can be factored as - MATH.format("(a+b)(a-b)", "normalsize", KhanUtil.BLUE). -

-

- First, determine the values of - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a=\\sqrt{"+a*a+"x^2}="+a+"x", "normalsize", KhanUtil.BLUE)

- MATH.format("b=\\sqrt{"+b*b+"}="+b, "normalsize", KhanUtil.BLUE) -

-

- Replace - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. -

-

- MATH.format("("+a+"x+"+b+")("+a+"x-"+b+")", "large", KhanUtil.ORANGE) -

+

+ Recognize that the expression is of the form + MATH.format("a^2-b^2", "normalsize", KhanUtil.BLUE) + , which can be factored as + MATH.format("(a+b)(a-b)", "normalsize", KhanUtil.BLUE). +

+

+ First, determine the values of + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a=\\sqrt{"+a*a+"x^2}="+a+"x", "normalsize", KhanUtil.BLUE)

+ MATH.format("b=\\sqrt{"+b*b+"}="+b, "normalsize", KhanUtil.BLUE) +

+

+ Replace + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. +

+

+ MATH.format("("+a+"x+"+b+")("+a+"x-"+b+")", "large", KhanUtil.ORANGE) +

+
+
-
-
121 exercises/factoring_polynomials_1.html
 @@ -1,121 +0,0 @@ - - - - - Factoring Polynomials - - - -
-
-
-
- MathModel.init() - randRangeExclude(-4, 4, [-1, 0, 1]) - randRange(5, 9) - randRange(1, 3) - randRange(1, 2) - randRange(1, 3) - randRange(1, 2) - a_val*b_val - b_val - MATH.parse(A+"u^"+(e_val+f_val)+"v^"+h_val+"+"+B+"u^"+f_val+"v^"+(g_val+h_val)) - MATH.parse("("+b_val+"u^"+f_val+"v^"+h_val+")("+a_val+"u^"+e_val+"+"+"v^"+g_val+")") -
-
-

- Factor the following expression: -

-

- MATH.format(PROBLEM,"large") -

- -
-
-
- Enter the result here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
3u^2v*(2u+3v^3)
-
3u^2v(2u+3v^3)
-
-
-
-

- Find the common factors of both terms of the expression. -

-

- - "\\large{" + - a_val + "\\cdot" + - "\\color{" + KhanUtil.BLUE + "}{" + b_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{u^" + f_val +"} \\cdot " + - "u^" + e_val + "\\cdot " + - "\\color{" + KhanUtil.BLUE + "}{v^" + h_val + "} + " + - "\\color{" + KhanUtil.BLUE + "}{" + b_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{u^" + f_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{v^" + h_val + "} \\cdot " + - "v^" + g_val + - "}" - -

-
- -
-

- Undistribute the common factor, dividing both terms by that common factor. -

-

- - "\\large{" + - "\\color{" + KhanUtil.BLACK + "}{" + b_val + "}" + - "\\color{" + KhanUtil.BLACK + "}{u^" + f_val +"}" + - "\\color{" + KhanUtil.BLACK + "}{v^" + h_val + "}" + - "\\cdot \\frac{("+ - a_val + "\\cdot" + - "\\color{" + KhanUtil.BLUE + "}{" + b_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{u^" + f_val +"} \\cdot " + - "u^" + e_val + "\\cdot " + - "\\color{" + KhanUtil.BLUE + "}{v^" + h_val + "} + " + - "\\color{" + KhanUtil.BLUE + "}{" + b_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{u^" + f_val + "} \\cdot " + - "\\color{" + KhanUtil.BLUE + "}{v^" + h_val + "} \\cdot " + - "v^" + g_val + ")" + - "}{"+ - "\\color{" + KhanUtil.BLUE + "}{" + b_val + "}" + - "\\color{" + KhanUtil.BLUE + "}{u^" + f_val +"}" + - "\\color{" + KhanUtil.BLUE + "}{v^" + h_val + "}" + - "}}" - -

-
- -
-

- And simplify to compute the answer. -

-

- - "\\large{" + - "\\color{" + KhanUtil.BLACK + "}{" + b_val + "}" + - "\\color{" + KhanUtil.BLACK + "}{u^" + f_val + "}" + - "\\color{" + KhanUtil.BLACK + "}{v^" + h_val + "}" + - "\\cdot (" + a_val + "u^" + e_val + "+v^" + g_val + ")" + - "}" - -

-
- -
-
-
-
- -
137 exercises/factoring_polynomials_by_grouping_1.html
 @@ -1,84 +1,87 @@ - - Factoring Polynomials by Grouping where A=1 - + + Factoring Polynomials by Grouping where A=1 + -
-
+
+
- MathModel.init() - randRangeNonZero(-4, 4) - randRange(6, 19) - a_val+b_val - a_val*b_val - MATH.polynomial([1, B, C], "x") - - MATH.parse("(x+"+a_val+")(x+"+b_val+")") + MathModel.init() + randRangeNonZero(-4, 4) + randRange(6, 19) + a_val+b_val + a_val*b_val + MATH.polynomial([1, B, C], "x") + + MATH.parse("(x+"+a_val+")(x+"+b_val+")")
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

+

+ Factor the following expression: +

+

+ MATH.format(PROBLEM, "large") +

-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(x+1)(x+2)
+
+ Enter the factored expression here:
+ +
+
jQuery( "div.instruction input" ).val()
+
+ return MATH.isEqual(MATH.parse(guess), SOLUTION) +
+
+
+
+ jQuery( "div.instruction input" ).val( guess ) +
+
(x+1)(x+2)
-

- Recognize that the expression is of the form - MATH.format("x^2+Bx+C", "normalsize", KhanUtil.BLUE) - , which can be factored by grouping. -

-

- Find the factors - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of - MATH.format("C="+C, "normalsize", KhanUtil.BLUE) whose sum is the value of - MATH.format("B="+B, "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+a_val, "normalsize", KhanUtil.BLUE)
- MATH.format("b="+b_val, "normalsize", KhanUtil.BLUE) -

-

- Rewrite the middle term of the original equation using these factors to form - two groups. -

-

- MATH.format("x^2+"+a_val+"x+"+b_val+"x+"+C, "normalsize", KhanUtil.BLUE) -

-

- Factor the first two terms terms and the second two terms. -

-

- MATH.format("x(x+"+a_val+")+"+b_val+"(x+"+a_val+")", "normalsize", KhanUtil.BLUE) -

-

- Redistribute the common term to get the answer. -

-

- MATH.format("(x+"+b_val+")(x+"+a_val+")", "large", KhanUtil.ORANGE) -

+

+ Recognize that the expression is of the form + MATH.format("x^2+Bx+C", "normalsize", KhanUtil.BLUE) + , which can be factored by grouping. +

+

+ Find the factors + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of + MATH.format("C="+C, "normalsize", KhanUtil.BLUE) whose sum is the value of + MATH.format("B="+B, "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a="+a_val, "normalsize", KhanUtil.BLUE)
+ MATH.format("b="+b_val, "normalsize", KhanUtil.BLUE) +

+

+ Rewrite the middle term of the original equation using these factors to form + two groups. +

+

+ MATH.format("x^2+"+a_val+"x+"+b_val+"x+"+C, "normalsize", KhanUtil.BLUE) +

+

+ Factor the first two terms terms and the second two terms. +

+

+ MATH.format("x(x+"+a_val+")+"+b_val+"(x+"+a_val+")", "normalsize", KhanUtil.BLUE) +

+

+ Redistribute the common term to get the answer. +

+

+ MATH.format("(x+"+b_val+")(x+"+a_val+")", "large", KhanUtil.ORANGE) +

+
+
-
-
149 exercises/factoring_polynomials_by_grouping_2.html
 @@ -1,90 +1,93 @@ - - Factoring Polynomials by Grouping where A != 1 - + + Factoring Polynomials by Grouping where A != 1 + -
-
+
+
- MathModel.init() - randRange(2, 9) - randFromArray([-1, 1]) - randFromArrayExclude([3, 5, 7, 9], [a]) - b_sign*b_abs - randFromArrayExclude(getFactors(a*b_abs), [1]) - a+b - a*b/A - getGCD(A, a) - b_sign*getGCD(b_abs, C) - MATH.polynomial([A, B, C], "x") - - MATH.parse("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")") - MATH.parse(F1+"x("+A/F1+"x+"+a/F1+")+"+F2+"("+b/F2+"x+"+C/F2+")") + MathModel.init() + randRange(2, 9) + randFromArray([-1, 1]) + randFromArrayExclude([3, 5, 7, 9], [a]) + b_sign*b_abs + randFromArrayExclude(getFactors(a*b_abs), [1]) + a+b + a*b/A + getGCD(A, a) + b_sign*getGCD(b_abs, C) + MATH.polynomial([A, B, C], "x") + + MATH.parse("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")") + MATH.parse(F1+"x("+A/F1+"x+"+a/F1+")+"+F2+"("+b/F2+"x+"+C/F2+")")
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

+

+ Factor the following expression: +

+

+ MATH.format(PROBLEM, "large") +

-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(x+1)(x+2)
+
+ Enter the factored expression here:
+ +
+
jQuery( "div.instruction input" ).val()
+
+ return MATH.isEqual(MATH.parse(guess), SOLUTION) +
+
+
+
+ jQuery( "div.instruction input" ).val( guess ) +
+
(x+1)(x+2)
-

- Recognize that the expression is of the form - MATH.format("Ax^2+Bx+C", "normalsize", KhanUtil.BLUE) - , which can be factored by grouping. -

-

- Find the factors - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of - MATH.format("A*C="+(A*C), "normalsize", KhanUtil.BLUE) whose sum is the value of - MATH.format("B="+B, "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+a, "normalsize", KhanUtil.BLUE)
- MATH.format("b="+b, "normalsize", KhanUtil.BLUE) -

-

- Rewrite the middle term of the original equation using these factors to form - two groups. -

-

- MATH.format(A+"x^2+"+a+"x+"+b+"x+"+C, "normalsize", KhanUtil.BLUE) -

-

- Factor the first two terms terms and the second two terms. -

-

- MATH.format(HINT1, "normalsize", KhanUtil.BLUE) -

-

- Redistribute the common term to get the answer. -

-

- MATH.format(SOLUTION, "large", KhanUtil.ORANGE) -

+

+ Recognize that the expression is of the form + MATH.format("Ax^2+Bx+C", "normalsize", KhanUtil.BLUE) + , which can be factored by grouping. +

+

+ Find the factors + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of + MATH.format("A*C="+(A*C), "normalsize", KhanUtil.BLUE) whose sum is the value of + MATH.format("B="+B, "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a="+a, "normalsize", KhanUtil.BLUE)
+ MATH.format("b="+b, "normalsize", KhanUtil.BLUE) +

+

+ Rewrite the middle term of the original equation using these factors to form + two groups. +

+

+ MATH.format(A+"x^2+"+a+"x+"+b+"x+"+C, "normalsize", KhanUtil.BLUE) +

+

+ Factor the first two terms terms and the second two terms. +

+

+ MATH.format(HINT1, "normalsize", KhanUtil.BLUE) +

+

+ Redistribute the common term to get the answer. +

+

+ MATH.format(SOLUTION, "large", KhanUtil.ORANGE) +

+
+
-
-
19 exercises/factoring_polynomials_challenge.html
 @@ -1,19 +0,0 @@ - - - - - Polynomial Factoring Challenge - - - -
-
-
-
-
-
-
-
-
- -
154 exercises/factoring_polynomials_to_solve_1.html
 @@ -1,96 +1,96 @@ - - Factoring Polynomials to Solve for the Unknown (A=1) - + + Factoring Polynomials to Solve for the Unknown (A=1) + -
-
+
+
- MathModel.init() - randRangeNonZero(-4, 4) - randRange(6, 19) - randRange(20, 29) - a_val+b_val - a_val*b_val - MATH.polynomial([1, B, C], "x") + MathModel.init() + randRangeNonZero(-4, 4) + randRange(6, 19) + randRange(20, 29) + a_val+b_val + a_val*b_val + MATH.polynomial([1, B, C], "x")
-

- Solve for x given the following equation: -

-

- MATH.format(PROBLEM, "large") -

+

+ Solve for x given the following equation: +

+

+ MATH.format(PROBLEM, "large") +

-
-a_val
-
-b_val
-
-

x = \quad\quad \text{or} \quad x = \quad

-
-
+
-a_val
+
-b_val
+
+

x = \quad\quad \text{or} \quad x = \quad

+
+
-

- Recognize that the left hand side expression is of the form - MATH.format("x^2+Bx+C", "normalsize", KhanUtil.BLUE) - , which can be factored by grouping. -

-

- Find the factors - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of - MATH.format("C="+C, "normalsize", KhanUtil.BLUE) whose sum is the value of - MATH.format("B="+B, "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+a_val, "normalsize", KhanUtil.BLUE)
- MATH.format("b="+b_val, "normalsize", KhanUtil.BLUE) -

-

- Rewrite the middle term of the original equation using these factors to form - two groups. -

-

- MATH.format("x^2+"+a_val+"x+"+b_val+"x+"+C+"=0", "normalsize", KhanUtil.BLUE) -

-

- Factor the first two terms terms and the second two terms. -

-

- MATH.format("x(x+"+a_val+")+"+b_val+"(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) -

-

- Redistribute the common term to get the answer. -

-

- MATH.format("(x+"+b_val+")(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) -

-

- Recall that for the left hand side to be equal to zero one or both of the terms being multiplied must be equal to zero. -

-

- MATH.format("(x+"+b_val+")=0", "normalsize", KhanUtil.BLUE)\quad - or - \quadMATH.format("(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) -

-

- Therefore the solutions are: -

-

- MATH.format("x="+(-b_val), "large", KhanUtil.GREEN)\quad - or - \quadMATH.format("x="+(-a_val), "large", KhanUtil.GREEN) -

+

+ Recognize that the left hand side expression is of the form + MATH.format("x^2+Bx+C", "normalsize", KhanUtil.BLUE) + , which can be factored by grouping. +

+

+ Find the factors + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of + MATH.format("C="+C, "normalsize", KhanUtil.BLUE) whose sum is the value of + MATH.format("B="+B, "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a="+a_val, "normalsize", KhanUtil.BLUE)
+ MATH.format("b="+b_val, "normalsize", KhanUtil.BLUE) +

+

+ Rewrite the middle term of the original equation using these factors to form + two groups. +

+

+ MATH.format("x^2+"+a_val+"x+"+b_val+"x+"+C+"=0", "normalsize", KhanUtil.BLUE) +

+

+ Factor the first two terms terms and the second two terms. +

+

+ MATH.format("x(x+"+a_val+")+"+b_val+"(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) +

+

+ Redistribute the common term to get the answer. +

+

+ MATH.format("(x+"+b_val+")(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) +

+

+ Recall that for the left hand side to be equal to zero one or both of the terms being multiplied must be equal to zero. +

+

+ MATH.format("(x+"+b_val+")=0", "normalsize", KhanUtil.BLUE)\quad + or + \quadMATH.format("(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE) +

+

+ Therefore the solutions are: +

+

+ MATH.format("x="+(-b_val), "large", KhanUtil.GREEN)\quad + or + \quadMATH.format("x="+(-a_val), "large", KhanUtil.GREEN) +

+
+
-
-
176 exercises/factoring_polynomials_to_solve_2.html
 @@ -1,107 +1,107 @@ - - Factoring Polynomials to Solve for the Unknown (A!=1) - + + Factoring Polynomials to Solve for the Unknown (A!=1) + -
-
+
+
- MathModel.init() - randRange(2, 9) - randFromArray([-1, 1]) - randFromArrayExclude([3, 5, 7, 9], [a]) - b_sign*b_abs - randFromArrayExclude(getFactors(a*b_abs), [1]) - a+b - a*b/A - getGCD(A, a) - b_sign*getGCD(b_abs, C) - MATH.polynomial([A, B, C], "x") - MATH.parse("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")=0") - MATH.parse(F1+"x("+A/F1+"x+"+a/F1+")+"+F2+"("+b/F2+"x+"+C/F2+")=0") - MATH.parse("x=1/2") - (-F2)/F1 - (-a/F1)/(A/F1) + MathModel.init() + randRange(2, 9) + randFromArray([-1, 1]) + randFromArrayExclude([3, 5, 7, 9], [a]) + b_sign*b_abs + randFromArrayExclude(getFactors(a*b_abs), [1]) + a+b + a*b/A + getGCD(A, a) + b_sign*getGCD(b_abs, C) + MATH.polynomial([A, B, C], "x") + MATH.parse("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")=0") + MATH.parse(F1+"x("+A/F1+"x+"+a/F1+")+"+F2+"("+b/F2+"x+"+C/F2+")=0") + MATH.parse("x=1/2") + (-F2)/F1 + (-a/F1)/(A/F1)
-

- Solve for x given the following equation: -

-

- MATH.format(PROBLEM, "large") -

+

+ Solve for x given the following equation: +

+

+ MATH.format(PROBLEM, "large") +

-
A1
-
A2
-
-

x = \quad +

A1
+
A2
+
+

x = \quad \quad \text{or} \quad x = \quad -

-
-
+

+
+
-

- Recognize that the left hand side expression is of the form - MATH.format("Ax^2+Bx+C", "normalsize", KhanUtil.BLUE) - , which can be factored by grouping. -

-

- Find the factors - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of - MATH.format("A*C="+(A*C), "normalsize", KhanUtil.BLUE) whose sum is the value of - MATH.format("B="+B, "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+a, "normalsize", KhanUtil.BLUE)
- MATH.format("b="+b, "normalsize", KhanUtil.BLUE) -

-

- Rewrite the middle term of the original equation using these factors to form - two groups. -

-

- MATH.format(A+"x^2+"+a+"x+"+b+"x+"+C+"=0", "normalsize", KhanUtil.BLUE) -

-

- Factor the first two terms terms and the second two terms. -

-

- MATH.format(HINT1, "normalsize", KhanUtil.BLUE) -

-

- Redistribute the common term to get the answer. -

-

- MATH.format("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")=0", "normalsize", KhanUtil.BLUE) -

-

- Recall that for the left hand side to be equal to zero one or both of the terms being multiplied must be equal to zero. - Therefore, if x satisfies either of the following equations it satisfies the original equation. -

-

- MATH.format(F1+"x+"+F2+"=0", "normalsize", KhanUtil.BLUE)\quad - or - \quadMATH.format(A/F1 + "x+" + a/F1 + "=0", "normalsize", KhanUtil.BLUE) -

-

- Solve for x in both equations. -

-

- MATH.format("x="+"-"+F2+"/"+F1, "normalsize", KhanUtil.GREEN)\quad - or - \quadMATH.format("x="+"-"+a/F1+"/"+A/F1, "normalsize", KhanUtil.GREEN) -

+

+ Recognize that the left hand side expression is of the form + MATH.format("Ax^2+Bx+C", "normalsize", KhanUtil.BLUE) + , which can be factored by grouping. +

+

+ Find the factors + MATH.format("a", "normalsize", KhanUtil.BLUE) and + MATH.format("b", "normalsize", KhanUtil.BLUE) of the value of + MATH.format("A*C="+(A*C), "normalsize", KhanUtil.BLUE) whose sum is the value of + MATH.format("B="+B, "normalsize", KhanUtil.BLUE). +

+

+ MATH.format("a="+a, "normalsize", KhanUtil.BLUE)
+ MATH.format("b="+b, "normalsize", KhanUtil.BLUE) +

+

+ Rewrite the middle term of the original equation using these factors to form + two groups. +

+

+ MATH.format(A+"x^2+"+a+"x+"+b+"x+"+C+"=0", "normalsize", KhanUtil.BLUE) +

+

+ Factor the first two terms terms and the second two terms. +

+

+ MATH.format(HINT1, "normalsize", KhanUtil.BLUE) +

+

+ Redistribute the common term to get the answer. +

+

+ MATH.format("("+F1+"x+"+F2+")("+A/F1+"x+"+a/F1+")=0", "normalsize", KhanUtil.BLUE) +

+

+ Recall that for the left hand side to be equal to zero one or both of the terms being multiplied must be equal to zero. + Therefore, if x satisfies either of the following equations it satisfies the original equation. +

+

+ MATH.format(F1+"x+"+F2+"=0", "normalsize", KhanUtil.BLUE)\quad + or + \quadMATH.format(A/F1 + "x+" + a/F1 + "=0", "normalsize", KhanUtil.BLUE) +

+

+ Solve for x in both equations. +

+

+ MATH.format("x="+"-"+F2+"/"+F1, "normalsize", KhanUtil.GREEN)\quad + or + \quadMATH.format("x="+"-"+a/F1+"/"+A/F1, "normalsize", KhanUtil.GREEN) +

+
+
-
-
72 exercises/factoring_special_polynomials_1.html
 @@ -1,72 +0,0 @@ - - - - - Factoring Perfect Square Polynomials with A = 1 - - - -
-
-
-
- MathModel.init() - randRangeNonZero(-9, 9) - 1 - 2*b - b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("(x+"+b+")^2") -
-
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

-
-
-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(x+2)^2
-
-
-

- Recognize that the expression is of the form - MATH.format("a^2+2ab+b^2", "normalsize", KhanUtil.BLUE) - , which can be factored as - MATH.format("(a+b)^2", "normalsize", KhanUtil.BLUE). -

-

- First, determine the values of - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+"x", "normalsize", KhanUtil.BLUE)

- MATH.format("b="+2*b+"/"+2+"="+b, "normalsize", KhanUtil.BLUE) -

-

- Replace - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. -

-

- MATH.format("(x+"+b+")^2", "large", KhanUtil.ORANGE) -

-
-
-
-
- -
73 exercises/factoring_special_polynomials_2.html
 @@ -1,73 +0,0 @@ - - - - - Factoring Special Product Polynomials with A != 1 - - - -
-
-
-
- MathModel.init() - randRange(2, 9) - randRangeNonZero(-9, 9) - a*a - 2*a*b - b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("("+a+"x+"+b+")^2") -
-
-

- Factor the following expression: -

-

- MATH.format(PROBLEM, "large") -

-
-
-
- Enter the factored expression here:
- -
-
window._guess
-
- return MATH.isEqual(MATH.parse(guess), SOLUTION) -
-
-
-
(2x+3)^2
-
-
-

- Recognize that the expression is of the form - MATH.format("a^2+2ab+b^2", "normalsize", KhanUtil.BLUE) - , which can be factored as - MATH.format("(a+b)^2", "normalsize", KhanUtil.BLUE). -

-

- First, determine the values of - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE). -

-

- MATH.format("a="+a+"x", "normalsize", KhanUtil.BLUE)

- MATH.format("b="+2*b+"/"+2+"="+b, "normalsize", KhanUtil.BLUE) -

-

- Replace - MATH.format("a", "normalsize", KhanUtil.BLUE) and - MATH.format("b", "normalsize", KhanUtil.BLUE) in the factored equation to find the answer. -

-

- MATH.format("("+a+"x+"+b+")^2", "large", KhanUtil.ORANGE) -

-
-
-
-
- -
58 exercises/polynomial_intuition_0.html
 @@ -1,58 +0,0 @@ - - - - - Polynomial Intuition - - - -
-
-
-
- MathModel.init() - randRange(0, 4) - randRangeNonZero(-1, 1) - MATH.parse(SIGN+"*x^"+DEGREE) -
-
-

- What is the degree of the polynomial function graphed below? -

-
- MATH.graph(P, BLUE, 17) -
-
-
- DEGREE -
-
-

- The degree of a polynomial determines the rate at which its value increases as a function - of its variable. -

-
-

- One way to determine the degree of polynomial function is by experimenting with different values - for its variable. In the graph above, we see that: -

-

- f(-2)=MATH.eval(P, {x:-2})
- f(-1)=MATH.eval(P, {x:-1})
- f(0)=MATH.eval(P, {x:0})
- f(1)=MATH.eval(P, {x:1})
- f(2)=MATH.eval(P, {x:2})
-

-
-

- The value of the function is changing at a rate of MATH.format("x^"+DEGREE). -

-

- Therefore we know that the polynomial function is of degree MATH.format(DEGREE). -

-
-
-
-
- -
156 exercises/polynomial_intuition_1.html
 @@ -1,156 +0,0 @@ - - - - - Polynomial Intuition 1 - - - -
-
-
-
- MathModel.init() - randRangeNonZero(-4, 4) - 1 - 2*b - b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("x^2+"+B+"x+"+C) -
-
-

- Write the polynomial expression that defines the function graphed below: -

-
- MATH.graph(P) -
-
-
-
- Enter the expression here:
- -
-
window._guess
-
- var isCorrect = MATH.isEqual(MATH.parse(guess), S); - MATH.graph(MATH.parse(guess), isCorrect?ORANGE:BLUE); - return isCorrect; -
-
-
-
x^2-6x+9
-
-
-

- First, recognize that the graph represents a polynomial of degree 2 because the - value of the expression increase with the square of the value of x. -

-

- Next, identify the point at which the graph crosses the x-axis, that is where f(x)=MATH.format("0", "normalsize", BLUE). -

-

- MATH.format("x=-"+b, "normalsize", BLUE) -

-
-

- Therefore we know that the function consists of some multiple of - MATH.format("(x+"+b+")^2", "normalsize", BLUE) which is equivalent to -

-

- MATH.format("x^2+"+B+"x+"+C, "normalsize", BLUE) -

-
-

- Next, identify the value of the expression when MATH.format("x = 0", "normalsize", BLUE) to determine - the point at which the graph crosses the y-axis. This will tell us if the above expression needs to be scaled by some multiple. -

-

- f(0)=MATH.format(C, "normalsize", BLUE) -

-
- So we know that the graph is of the function: -

-

- f(x)=MATH.format("x^2+"+B+"x+"+C, "large", ORANGE). -

-
-
-
-
-
- MathModel.init() - randRange(1, 2) - randRangeNonZero(-1, 1) - 1 - 0 - -b*b - MATH.polynomial([A, B, C], "x") - - MATH.parse("x^2+"+C) -
-
-

- Write the polynomial expression that defines the function graphed below: -

-
- MATH.graph(P) -
-
-
-
- Enter the expression here:
- -
-
window._guess
-
- var isCorrect = MATH.isEqual(MATH.parse(guess), S); - MATH.graph(MATH.parse(guess), isCorrect?ORANGE:BLUE); - return isCorrect; -
-
-
-
x^2-6x+9
-
-
-

- First, recognize that the graph represents a polynomial of degree 2 because the - value of the expression increase with the square of the value of x. -

-

- Next, identify the points at which the graph crosses the x-axis, that is where f(x)=MATH.format("0", "normalsize", BLUE). -

-

- MATH.format("x="+b, "normalsize", BLUE) and - MATH.format("x=-"+b, "normalsize", BLUE) -

-
-

- Therefore we know that the function consists of some multiple of - MATH.format("(x+"+b+")(x-"+b+")", "normalsize", BLUE) which is equivalent to -

-

- MATH.format("x^2+"+C, "normalsize", BLUE) -

-
-

- Next, identify the value of the expression when MATH.format("x = 0", "normalsize", BLUE) to determine - the point at which the graph crosses the y-axis. This will tell us if the above expression needs to be scaled by some multiple. -

-

- f(0)=MATH.format(C, "normalsize", BLUE) -

-
- So we know that the graph is of the function: -

-

- f(x)=MATH.format("x^2+"+C, "large", ORANGE). -

-
-
-
-
-
- -

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