Question

Factor:$-4b^2+16b$

Short answer

The required factor is$-4b\left(b-4\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$-4b^2+16b$

Step 2. Find the GCF.

Find the GCF of $4b^2\mathrm{and}16b$,

$$\begin{gathered} 4b^2=2·2·b·b \\ 16b=2·2·2·2·b \end{gathered}$$

GCF is:

localid="1647713925251" role="math" $$\begin{gathered} =2·2·b \\ =4b \end{gathered}$$

Since the leading coefficient is negative, the GCF is negative,localid="1647713725349" $-4b$.

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$-4b·b-\left(-4b\right)·4$

Factor the GCF,

$-4b\left(b-4\right)$