Question

factor $18u^4v^2 + 30uv$.
a. $3u(3u^3v^2 + 5v)$
b. $6u(3u^3v^2 - 5v)$
c. $-6u(3u^3v^2 + 5v)$
d. $6uv(3u^3v + 5)$

Explanation:

Step1: Find GCF of coefficients

GCF of 18 and 30 is 6.

Step2: Find GCF of variables

For $u$: lowest power is $u^1$; for $v$: lowest power is $v^1$. So GCF is $uv$.

Step3: Factor out overall GCF

Overall GCF is $6uv$. Divide each term:
$\frac{18u^4v^2}{6uv}=3u^3v$, $\frac{30uv}{6uv}=5$
Result: $6uv(3u^3v + 5)$

Answer:

d. $6uv(3u^3v + 5)$