Factor 2p^3-12p^2-54p

$2 p^{3} - 12 p^{2} - 54 p$

Step 1

Factor $2 p$ out of $2 p^{3} - 12 p^{2} - 54 p$ .

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

$2 p (p^{2}) - 12 p^{2} - 54 p$

Factor $2 p$ out of $- 12 p^{2}$ .

$2 p (p^{2}) + 2 p (- 6 p) - 54 p$

Factor $2 p$ out of $- 54 p$ .

$2 p (p^{2}) + 2 p (- 6 p) + 2 p (- 27)$

Factor $2 p$ out of $2 p (p^{2}) + 2 p (- 6 p)$ .

$2 p (p^{2} - 6 p) + 2 p (- 27)$

Factor $2 p$ out of $2 p (p^{2} - 6 p) + 2 p (- 27)$ .

$2 p (p^{2} - 6 p - 27)$

Step 2

Factor.

Factor $p^{2} - 6 p - 27$ 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 $- 27$ and whose sum is $- 6$ .

$- 9, 3$

Write the factored form using these integers.

$2 p ((p - 9) (p + 3))$

Remove unnecessary parentheses.

$2 p (p - 9) (p + 3)$

Factor 2p^3-12p^2-54p

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