Trigonometry Examples

$4 p^{3} + 24 p^{2} - 64 p$

Step 1

Factor $4 p$ out of $4 p^{3} + 24 p^{2} - 64 p$ .

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Step 1.1

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

$4 p (p^{2}) + 24 p^{2} - 64 p$

Step 1.2

Factor $4 p$ out of $24 p^{2}$ .

$4 p (p^{2}) + 4 p (6 p) - 64 p$

Step 1.3

Factor $4 p$ out of $- 64 p$ .

$4 p (p^{2}) + 4 p (6 p) + 4 p (- 16)$

Step 1.4

Factor $4 p$ out of $4 p (p^{2}) + 4 p (6 p)$ .

$4 p (p^{2} + 6 p) + 4 p (- 16)$

Step 1.5

Factor $4 p$ out of $4 p (p^{2} + 6 p) + 4 p (- 16)$ .

$4 p (p^{2} + 6 p - 16)$

Step 2

Factor.

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Step 2.1

Factor $p^{2} + 6 p - 16$ using the AC method.

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Step 2.1.1

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 $- 16$ and whose sum is $6$ .

$- 2, 8$

Step 2.1.2

Write the factored form using these integers.

$4 p ((p - 2) (p + 8))$

Step 2.2

Remove unnecessary parentheses.

$4 p (p - 2) (p + 8)$