Question

1. factor $30a^{3}b^{2}-80a^{3}+10a^{6}$.

a. $a^{3}(30b^{2}-80+a^{3})$
b. $10a^{3}(3b^{2}-8)$
c. $10a^{3}(3b^{2}-8+a^{3})$
d. $10a^{3}(b^{2}-8)$

Explanation:

Step1: Find GCF of coefficients

GCF of 30, 80, 10 is 10.

Step2: Find GCF of variable terms

GCF of $a^3b^2$, $a^3$, $a^6$ is $a^3$.

Step3: Factor out overall GCF

Factor $10a^3$ from each term:
$30a^3b^2 - 80a^3 + 10a^6 = 10a^3(3b^2 - 8 + a^3)$

Answer:

c. $10a^3(3b^2 - 8 + a^3)$