Simplify (x^3+5x^2)/(x^2+x-20)

$\frac{x^{3} + 5 x^{2}}{x^{2} + x - 20}$

Step 1

Factor $x^{2}$ out of $x^{3} + 5 x^{2}$ .

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

$\frac{x^{2} x + 5 x^{2}}{x^{2} + x - 20}$

Factor $x^{2}$ out of $5 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 5}{x^{2} + x - 20}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 5$ .

$\frac{x^{2} (x + 5)}{x^{2} + x - 20}$

Step 2

Factor $x^{2} + x - 20$ 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 $- 20$ and whose sum is $1$ .

$- 4, 5$

Write the factored form using these integers.

$\frac{x^{2} (x + 5)}{(x - 4) (x + 5)}$

Step 3

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{x^{2} (x + 5)}{(x - 4) (x + 5)}$

Rewrite the expression.

$\frac{x^{2}}{x - 4}$

Simplify (x^3+5x^2)/(x^2+x-20)

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