Factor 5x^3-20x^2+15x

$5 x^{3} - 20 x^{2} + 15 x$

Step 1

Factor $5 x$ out of $5 x^{3} - 20 x^{2} + 15 x$ .

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

$5 x (x^{2}) - 20 x^{2} + 15 x$

Factor $5 x$ out of $- 20 x^{2}$ .

$5 x (x^{2}) + 5 x (- 4 x) + 15 x$

Factor $5 x$ out of $15 x$ .

$5 x (x^{2}) + 5 x (- 4 x) + 5 x (3)$

Factor $5 x$ out of $5 x (x^{2}) + 5 x (- 4 x)$ .

$5 x (x^{2} - 4 x) + 5 x (3)$

Factor $5 x$ out of $5 x (x^{2} - 4 x) + 5 x (3)$ .

$5 x (x^{2} - 4 x + 3)$

Step 2

Factor.

Factor $x^{2} - 4 x + 3$ 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 $3$ and whose sum is $- 4$ .

$- 3, - 1$

Write the factored form using these integers.

$5 x ((x - 3) (x - 1))$

Remove unnecessary parentheses.

$5 x (x - 3) (x - 1)$

Factor 5x^3-20x^2+15x

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