Factor 5x^3-30x^2+40x

$5 x^{3} - 30 x^{2} + 40 x$

Step 1

Factor $5 x$ out of $5 x^{3} - 30 x^{2} + 40 x$ .

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

$5 x (x^{2}) - 30 x^{2} + 40 x$

Factor $5 x$ out of $- 30 x^{2}$ .

$5 x (x^{2}) + 5 x (- 6 x) + 40 x$

Factor $5 x$ out of $40 x$ .

$5 x (x^{2}) + 5 x (- 6 x) + 5 x (8)$

Factor $5 x$ out of $5 x (x^{2}) + 5 x (- 6 x)$ .

$5 x (x^{2} - 6 x) + 5 x (8)$

Factor $5 x$ out of $5 x (x^{2} - 6 x) + 5 x (8)$ .

$5 x (x^{2} - 6 x + 8)$

Step 2

Factor.

Factor $x^{2} - 6 x + 8$ 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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$5 x ((x - 4) (x - 2))$

Remove unnecessary parentheses.

$5 x (x - 4) (x - 2)$

Factor 5x^3-30x^2+40x

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