Factor 4x^3-32x^2+60x

$4 x^{3} - 32 x^{2} + 60 x$

Step 1

Factor $4 x$ out of $4 x^{3} - 32 x^{2} + 60 x$ .

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

$4 x (x^{2}) - 32 x^{2} + 60 x$

Factor $4 x$ out of $- 32 x^{2}$ .

$4 x (x^{2}) + 4 x (- 8 x) + 60 x$

Factor $4 x$ out of $60 x$ .

$4 x (x^{2}) + 4 x (- 8 x) + 4 x (15)$

Factor $4 x$ out of $4 x (x^{2}) + 4 x (- 8 x)$ .

$4 x (x^{2} - 8 x) + 4 x (15)$

Factor $4 x$ out of $4 x (x^{2} - 8 x) + 4 x (15)$ .

$4 x (x^{2} - 8 x + 15)$

Step 2

Factor.

Factor $x^{2} - 8 x + 15$ 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Write the factored form using these integers.

$4 x ((x - 5) (x - 3))$

Remove unnecessary parentheses.

$4 x (x - 5) (x - 3)$

Factor 4x^3-32x^2+60x

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