Question

factor the polynomial.
$12a^{3}b^{7}+3ab^{5}-15ab^{8}$
$12a^{3}b^{7}+3ab^{5}-15ab^{8} = \square$

Explanation:

Step1: Find the GCF of terms

GCF of $12, 3, -15$ is $3$; GCF of $a^3, a, a$ is $a$; GCF of $b^7, b^5, b^8$ is $b^5$. Overall GCF: $3ab^5$

Step2: Factor out the GCF

Divide each term by $3ab^5$:
$\frac{12a^3b^7}{3ab^5} = 4a^2b^2$, $\frac{3ab^5}{3ab^5} = 1$, $\frac{-15ab^8}{3ab^5} = -5b^3$
Expression: $3ab^5(4a^2b^2 + 1 - 5b^3)$

Answer:

$3ab^5(4a^2b^2 - 5b^3 + 1)$