Q. 342 - Intermediate Algebra

Question

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

$6y^2+12y-6$

Step-by-Step Solution

Answer

The factored form of the polynomial is $6\left(y^2+2y-1\right)$.

Step 1. Given information.

The polynomial is,

$6y^2+12y-6$ 

Step 2. Finding the greatest common factor.

Now, the greatest common factor for the given polynomial will be

$$\begin{gathered} 6y^2+12y-6 \\ \Rightarrow 6y^2=2\times 3\times y\times y \\ \Rightarrow 12y=2\times 2\times 3\times y \\ \Rightarrow 6=2\times 3 \end{gathered}$$

Then the greatest common factor is $6$.

Step 3. Factoring the polynomial.

Now using the distributive property factor the polynomial.

$6y^2+12y-6=6\left(y^2+2y-1\right)$

Hence, the simplified polynomial is $6(y^2+2y-1)$.

Step 4. Checking the result.

Multiplying the factors then we get

$6(y^2+2y-1)=6y^2+12y-6$.