Simplify (x^3+7x^2)/(x^2+2x-35)

$\frac{x^{3} + 7 x^{2}}{x^{2} + 2 x - 35}$

Step 1

Factor $x^{2}$ out of $x^{3} + 7 x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} x + 7 x^{2}}{x^{2} + 2 x - 35}$

Factor $x^{2}$ out of $7 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 7}{x^{2} + 2 x - 35}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 7$ .

$\frac{x^{2} (x + 7)}{x^{2} + 2 x - 35}$

Step 2

Factor $x^{2} + 2 x - 35$ 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 $- 35$ and whose sum is $2$ .

$- 5, 7$

Write the factored form using these integers.

$\frac{x^{2} (x + 7)}{(x - 5) (x + 7)}$

Step 3

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{x^{2} (x + 7)}{(x - 5) (x + 7)}$

Rewrite the expression.

$\frac{x^{2}}{x - 5}$

Simplify (x^3+7x^2)/(x^2+2x-35)

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