Question

In the following exercises, factor the greatest common factor from each polynomial.

$4y^2+8y-4$

Short answer

The required answer is$4\left(y^2+2y-1\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$4y^2+8y-4$

Step 2. Factor the greatest common factor from the polynomial.

Find the GCF of $4y^2,8y,\mathrm{and}4$,

$$\begin{gathered} 4y^2=2·2·y·y \\ 8y=2·2·2·y \\ 4=2·2 \end{gathered}$$

GCF is:

$$\begin{gathered} =2·2 \\ =4 \end{gathered}$$

Rewrite each term as a product using the GCF,

$4·y^2+4·2y-4·1$

Factor the GCF,

$4\left(y^2+2y-1\right)$