Factor g(x)=4x^3-8x^2-25x+50

$g (x) = 4 x^{3} - 8 x^{2} - 25 x + 50$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$g (x) = (4 x^{3} - 8 x^{2}) - 25 x + 50$

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

$g (x) = 4 x^{2} (x - 2) - 25 (x - 2)$

Step 2

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

$g (x) = (x - 2) (4 x^{2} - 25)$

Step 3

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$g (x) = (x - 2) ({(2 x)}^{2} - 25)$

Step 4

Rewrite $25$ as $5^{2}$ .

$g (x) = (x - 2) ({(2 x)}^{2} - 5^{2})$

Step 5

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 5$ .

$g (x) = (x - 2) ((2 x + 5) (2 x - 5))$

Remove unnecessary parentheses.

$g (x) = (x - 2) (2 x + 5) (2 x - 5)$