Question

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

$8p^2+4p+2$

Short answer

The factored form is$\begin{array}{rcl}& & 2(4p^2+2p+1)\end{array}$.

Step-by-step solution

Step 1. Given Information

The given polynomial is$8p^2+4p+2$.

Step 2. Find the GCF of the terms   

• Factor each of the terms in the given expression.

$$\begin{gathered} 8p^2=2·2·2·p·p \\ 4p=2·2·p \\ 2=2·1 \end{gathered}$$

• From the obtained factors, it is observed that the common factor is 2.
• So, the GCF of the terms of the given expression is 2.

Step 3. Rewrite the given expression   

• Express each of the term of the given expression as a product of GCF, 2.

$2·4p^2+2·2p+2·1$

• Use the reverse distributive property, $ab+ac=a(b+c)$to rewrite the obtained expression.

$2·4p^2+2·2p+2·1=2(4p^2+2p+1)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}2(4p^2+2p+1)& =& 2·4p^2+2·2p+2·1\\ & =& 8p^2+4p+2\end{array}$

• Since the obtained expression is the same as the given expression, the obtained factors are verified.