Question

Factor completely.15u^4-20u^3-35u^2

Answer 1

First of all, we can factor a factor of $5$ from all terms:

$5 (3u^4-4u^3-7u^2)$

Then, we can factor $u^2$ from all terms:

$5u^2 (3u^2-4u-7)$

To factor the quadratic expression in parenthesis, we must find its roots, which are $-1$ and $\frac{7}{3}$. This implies

$3u^2-4u-7 = 3(u+1)(u-\frac{7}{3})$

So, the complete factorization is

$5u^2 \cdot 3(u+1)(u-\frac{7}{3}) = 15u^2(u+1)(u-\frac{7}{3})$