Simplify (4x^3-36x^2)/(x^2-14x+45)

$\frac{4 x^{3} - 36 x^{2}}{x^{2} - 14 x + 45}$

Step 1

Factor $4 x^{2}$ out of $4 x^{3} - 36 x^{2}$ .

Factor $4 x^{2}$ out of $4 x^{3}$ .

$\frac{4 x^{2} (x) - 36 x^{2}}{x^{2} - 14 x + 45}$

Factor $4 x^{2}$ out of $- 36 x^{2}$ .

$\frac{4 x^{2} (x) + 4 x^{2} (- 9)}{x^{2} - 14 x + 45}$

Factor $4 x^{2}$ out of $4 x^{2} (x) + 4 x^{2} (- 9)$ .

$\frac{4 x^{2} (x - 9)}{x^{2} - 14 x + 45}$

Step 2

Factor $x^{2} - 14 x + 45$ 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 $45$ and whose sum is $- 14$ .

$- 9, - 5$

Write the factored form using these integers.

$\frac{4 x^{2} (x - 9)}{(x - 9) (x - 5)}$

Step 3

Cancel the common factor of $x - 9$ .

Cancel the common factor.

$\frac{4 x^{2} (x - 9)}{(x - 9) (x - 5)}$

Rewrite the expression.

$\frac{4 x^{2}}{x - 5}$

Simplify (4x^3-36x^2)/(x^2-14x+45)

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