Factor 8x^3-12x^2+4x

$8 x^{3} - 12 x^{2} + 4 x$

Step 1

Factor $4 x$ out of $8 x^{3} - 12 x^{2} + 4 x$ .

Factor $4 x$ out of $8 x^{3}$ .

$4 x (2 x^{2}) - 12 x^{2} + 4 x$

Factor $4 x$ out of $- 12 x^{2}$ .

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

Factor $4 x$ out of $4 x$ .

$4 x (2 x^{2}) + 4 x (- 3 x) + 4 x (1)$

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

$4 x (2 x^{2} - 3 x) + 4 x (1)$

Factor $4 x$ out of $4 x (2 x^{2} - 3 x) + 4 x (1)$ .

$4 x (2 x^{2} - 3 x + 1)$

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = - 3$ .

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

$4 x (2 x^{2} - 3 (x) + 1)$

Rewrite $- 3$ as $- 1$ plus $- 2$

$4 x (2 x^{2} + (- 1 - 2) x + 1)$

Apply the distributive property.

$4 x (2 x^{2} - 1 x - 2 x + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 x ((2 x^{2} - 1 x) - 2 x + 1)$

Factor out the greatest common factor (GCF) from each group.

$4 x (x (2 x - 1) - (2 x - 1))$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$4 x ((2 x - 1) (x - 1))$

Remove unnecessary parentheses.

$4 x (2 x - 1) (x - 1)$

Factor 8x^3-12x^2+4x

Related Questions

Support LCMGCF.com by disabling your adblocker.