Factor 15x^5-72x^3-108x

$15 x^{5} - 72 x^{3} - 108 x$

Step 1

Factor $3 x$ out of $15 x^{5} - 72 x^{3} - 108 x$ .

Factor $3 x$ out of $15 x^{5}$ .

$3 x (5 x^{4}) - 72 x^{3} - 108 x$

Factor $3 x$ out of $- 72 x^{3}$ .

$3 x (5 x^{4}) + 3 x (- 24 x^{2}) - 108 x$

Factor $3 x$ out of $- 108 x$ .

$3 x (5 x^{4}) + 3 x (- 24 x^{2}) + 3 x (- 36)$

Factor $3 x$ out of $3 x (5 x^{4}) + 3 x (- 24 x^{2})$ .

$3 x (5 x^{4} - 24 x^{2}) + 3 x (- 36)$

Factor $3 x$ out of $3 x (5 x^{4} - 24 x^{2}) + 3 x (- 36)$ .

$3 x (5 x^{4} - 24 x^{2} - 36)$

Step 2

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

$3 x (5 {(x^{2})}^{2} - 24 x^{2} - 36)$

Step 3

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$3 x (5 u^{2} - 24 u - 36)$

Step 4

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 $a \cdot c = 5 \cdot - 36 = - 180$ and whose sum is $b = - 24$ .

Factor $- 24$ out of $- 24 u$ .

$3 x (5 u^{2} - 24 (u) - 36)$

Rewrite $- 24$ as $6$ plus $- 30$

$3 x (5 u^{2} + (6 - 30) u - 36)$

Apply the distributive property.

$3 x (5 u^{2} + 6 u - 30 u - 36)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 x ((5 u^{2} + 6 u) - 30 u - 36)$

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

$3 x (u (5 u + 6) - 6 (5 u + 6))$

Factor the polynomial by factoring out the greatest common factor, $5 u + 6$ .

$3 x ((5 u + 6) (u - 6))$

Step 5

Factor.

Replace all occurrences of $u$ with $x^{2}$ .

$3 x ((5 x^{2} + 6) (x^{2} - 6))$

Remove unnecessary parentheses.

$3 x (5 x^{2} + 6) (x^{2} - 6)$

Factor 15x^5-72x^3-108x

Related Questions

Support LCMGCF.com by disabling your adblocker.