Factor 2x^3-14x^2+20x

$2 x^{3} - 14 x^{2} + 20 x$

Step 1

Factor $2 x$ out of $2 x^{3} - 14 x^{2} + 20 x$ .

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

$2 x (x^{2}) - 14 x^{2} + 20 x$

Factor $2 x$ out of $- 14 x^{2}$ .

$2 x (x^{2}) + 2 x (- 7 x) + 20 x$

Factor $2 x$ out of $20 x$ .

$2 x (x^{2}) + 2 x (- 7 x) + 2 x (10)$

Factor $2 x$ out of $2 x (x^{2}) + 2 x (- 7 x)$ .

$2 x (x^{2} - 7 x) + 2 x (10)$

Factor $2 x$ out of $2 x (x^{2} - 7 x) + 2 x (10)$ .

$2 x (x^{2} - 7 x + 10)$

Step 2

Factor.

Factor $x^{2} - 7 x + 10$ 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 $10$ and whose sum is $- 7$ .

$- 5, - 2$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Factor 2x^3-14x^2+20x

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