# Khan/khan-exercises

delete some exercises

1 parent 4f5dd17 commit ba18a0640b4d70e5d15f9abc46eb25c9a0fbfba8 petercollingridge committed Feb 15, 2013
 @@ -2,37 +2,45 @@ - Dividing polynomials by binomials + Adding and subtracting with like denominators +
-
- randRangeNonZero( -10, 10 ) - randRangeNonZero( -10, 10 ) -
- 1 - SQUARE*A*B - A*B - SQUARE*(-A-B) - -A-B + randRangeNonZero( -12, 12 ) + randRange( 1, 12 ) + randRange( 1, 12 ) + randVar() + randRange( 2, 12 ) + toFraction((COEFFICIENT1 + COEFFICIENT2) / DENOMINATOR)
-

Simplify the following expression:

-

\dfrac{plus(SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT}{x + -A}

+

Simplify the expression.

+

+ + \frac{COEFFICIENT1X + CONSTANT}{DENOMINATORX} + + \frac{COEFFICIENT2X - CONSTANT}{DENOMINATORX} + +

-
-
^\s*[xX]\s*B < 0 ? "\\+" : "[-\u2212]"\s*abs( B )\s*$- ^\s*B < 0 ? "" : "[-\u2212]"\s*abs( B )\s*\+\s*[xX]\s*$
-
-
an expression, like x+1
-
+

SOLUTION[0] / SOLUTION[1]

-

First factor the polynomial in the numerator.

When we factor a polynomial, we are basically reversing this process of multiplying linear expressions together:

@@ -83,18 +91,10 @@

-

- So we can rewrite the expression as: - - \dfrac{(x A < 0 ? "+" : "" \color{PINK}{-A}) - (x B < 0 ? "+" : "" \color{PINK}{-B})} - {x + -A} - -

- -

We can now divide the numerator and denominator by (x + -A).

- -

Which leaves us with x + -B.

+

+ So we can factor the expression as: (x A < 0 ? "+" : "" \color{PINK}{-A}) + (x B < 0 ? "+" : "" \color{PINK}{-B}) +

 @@ -11,19 +11,19 @@
+ randVar()
randRangeNonZero( -9, 9 )
- 1 -A * A

Simplify the following expression:

-

\dfrac{x^2 + CONSTANT}{x + A}

+

\dfrac{X^2 + CONSTANT}{X + A}

-
^\s*[xX]\s*A < 0 ? "\\+" : "[-\u2212]"\s*abs( A )\s*$- ^\s*A < 0 ? "" : "[-\u2212]"\s*abs( A )\s*\+\s*[xX]\s*$
+
^\s*X\s*A < 0 ? "\\+" : "[-\u2212]"\s*abs( A )\s*$+ ^\s*A < 0 ? "" : "[-\u2212]"\s*abs( A )\s*\+\s*X\s*$
an expression, like x+1
@@ -37,62 +37,60 @@

-

+

\qquad b = \sqrt{A * A} = A

So we can rewrite the expression as: - \dfrac{(\color{BLUE}{x} A > 0 ? "+" : "" \color{PINK}{A}) - (\color{BLUE}{x} A < 0 ? "+" : "" \color{PINK}{-A})} - {x + A} + \dfrac{(\color{BLUE}{X} A > 0 ? "+" : "" \color{PINK}{A}) + (\color{BLUE}{X} A < 0 ? "+" : "" \color{PINK}{-A})} + {X + A}

-

We can now divide the numerator and denominator by (x + A).

+

We can now divide the numerator and denominator by (X + A).

-

Which leaves us with x + -A.

+

Which leaves us with X + -A.

+ randVar()
randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 )
- 1 - SQUARE*A*B - A*B - SQUARE*(-A-B) - -A-B + A*B + -A-B

Simplify the following expression:

-

\dfrac{plus(SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT}{x + -A}

+

\dfrac{X^2 + plus( LINEAR + X ) + CONSTANT}{X + -A}

-
^\s*[xX]\s*B < 0 ? "\\+" : "[-\u2212]"\s*abs( B )\s*$- ^\s*B < 0 ? "" : "[-\u2212]"\s*abs( B )\s*\+\s*[xX]\s*$
+
^\s*X\s*B < 0 ? "\\+" : "[-\u2212]"\s*abs( B )\s*$+ ^\s*B < 0 ? "" : "[-\u2212]"\s*abs( B )\s*\+\s*X\s*$
an expression, like x+1

- plus(SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT = (x + -A)(x + -B) + X^2 + plus( LINEAR + X ) + CONSTANT = (X + -A)(X + -B)

So we can rewrite the expression as: - \dfrac{(x + -A)(x + -B)}{x + -A} + \dfrac{(X + -A)(X + -B)}{X + -A}

-

We can now divide the numerator and denominator by (x + -A).

+

We can now divide the numerator and denominator by (X + -A).

-

Which leaves us with x + -B.

+

Which leaves us with X + -B.