Factor 3x^5+6x^4-72x^3

$3 x^{5} + 6 x^{4} - 72 x^{3}$

Step 1

Factor $3 x^{3}$ out of $3 x^{5} + 6 x^{4} - 72 x^{3}$ .

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

$3 x^{3} (x^{2}) + 6 x^{4} - 72 x^{3}$

Factor $3 x^{3}$ out of $6 x^{4}$ .

$3 x^{3} (x^{2}) + 3 x^{3} (2 x) - 72 x^{3}$

Factor $3 x^{3}$ out of $- 72 x^{3}$ .

$3 x^{3} (x^{2}) + 3 x^{3} (2 x) + 3 x^{3} (- 24)$

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

$3 x^{3} (x^{2} + 2 x) + 3 x^{3} (- 24)$

Factor $3 x^{3}$ out of $3 x^{3} (x^{2} + 2 x) + 3 x^{3} (- 24)$ .

$3 x^{3} (x^{2} + 2 x - 24)$

Step 2

Factor.

Factor $x^{2} + 2 x - 24$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Write the factored form using these integers.

$3 x^{3} ((x - 4) (x + 6))$

Remove unnecessary parentheses.

$3 x^{3} (x - 4) (x + 6)$

Factor 3x^5+6x^4-72x^3

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