diff --git a/exercises/factoring_polynomials_to_solve_1.html b/exercises/factoring_polynomials_to_solve_1.html new file mode 100644 index 000000000..d45de680b --- /dev/null +++ b/exercises/factoring_polynomials_to_solve_1.html @@ -0,0 +1,96 @@ + + +
+ ++ Solve for x given the following equation: +
+
+ MATH.format(PROBLEM, "large")
+
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)
+ or
+ MATH.format("(x+"+a_val+")=0", "normalsize", KhanUtil.BLUE)
+
+ Therefore the solutions are: +
+
+ MATH.format("x="+(-b_val), "large", KhanUtil.GREEN)
+ or
+ MATH.format("x="+(-a_val), "large", KhanUtil.GREEN)
+
+ Solve for x given the following equation: +
+
+ MATH.format(PROBLEM, "large")
+
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)
+ MATH.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)
+