Factor 3x^3+9x^2-54x

$3 x^{3} + 9 x^{2} - 54 x$

Step 1

Factor $3 x$ out of $3 x^{3} + 9 x^{2} - 54 x$ .

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

$3 x (x^{2}) + 9 x^{2} - 54 x$

Factor $3 x$ out of $9 x^{2}$ .

$3 x (x^{2}) + 3 x (3 x) - 54 x$

Factor $3 x$ out of $- 54 x$ .

$3 x (x^{2}) + 3 x (3 x) + 3 x (- 18)$

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

$3 x (x^{2} + 3 x) + 3 x (- 18)$

Factor $3 x$ out of $3 x (x^{2} + 3 x) + 3 x (- 18)$ .

$3 x (x^{2} + 3 x - 18)$

Step 2

Factor.

Factor $x^{2} + 3 x - 18$ 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 $- 18$ and whose sum is $3$ .

$- 3, 6$

Write the factored form using these integers.

$3 x ((x - 3) (x + 6))$

Remove unnecessary parentheses.

$3 x (x - 3) (x + 6)$

Factor 3x^3+9x^2-54x

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