Simplify (2x^2+20x+32)/(x^2-2x-80)

$\frac{2 x^{2} + 20 x + 32}{x^{2} - 2 x - 80}$

Step 1

Simplify the numerator.

Factor $2$ out of $2 x^{2} + 20 x + 32$ .

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x^{2}) + 20 x + 32}{x^{2} - 2 x - 80}$

Factor $2$ out of $20 x$ .

$\frac{2 (x^{2}) + 2 (10 x) + 32}{x^{2} - 2 x - 80}$

Factor $2$ out of $32$ .

$\frac{2 x^{2} + 2 (10 x) + 2 \cdot 16}{x^{2} - 2 x - 80}$

Factor $2$ out of $2 x^{2} + 2 (10 x)$ .

$\frac{2 (x^{2} + 10 x) + 2 \cdot 16}{x^{2} - 2 x - 80}$

Factor $2$ out of $2 (x^{2} + 10 x) + 2 \cdot 16$ .

$\frac{2 (x^{2} + 10 x + 16)}{x^{2} - 2 x - 80}$

Factor $x^{2} + 10 x + 16$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $16$ and whose sum is $10$ .

$2, 8$

Write the factored form using these integers.

$\frac{2 ((x + 2) (x + 8))}{x^{2} - 2 x - 80}$

$\frac{2 (x + 2) (x + 8)}{x^{2} - 2 x - 80}$

Step 2

Factor $x^{2} - 2 x - 80$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 80$ and whose sum is $- 2$ .

$- 10, 8$

Write the factored form using these integers.

$\frac{2 (x + 2) (x + 8)}{(x - 10) (x + 8)}$

Step 3

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{2 (x + 2) (x + 8)}{(x - 10) (x + 8)}$

Rewrite the expression.

$\frac{2 (x + 2)}{x - 10}$

Simplify (2x^2+20x+32)/(x^2-2x-80)

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