Question

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

$8m^2-40m+16$

Short answer

The factored form is$\begin{array}{rcl}& & 8(m^2-5m+2)\end{array}$.

Step-by-step solution

Step 1. Given Information

The given polynomial is$8m^2-40m+16$.

Step 2. Find the GCF of the terms   

• Factor each of the terms in the given expression.

$$\begin{gathered} 8m^2=2·2·2·m·m \\ 40m=2·2·2·5·m \\ 16=2·2·2·2 \end{gathered}$$

• From the obtained factors, it is observed that the common factors are $2,2,2$.
• Multiply the common factors.

$2·2·2=8$

• So, the GCF of the terms of the given expression is 8.

Step 3. Rewrite the given expression     

• Express each of the term of the given expression as a product of GCF, 8.

$8·m^2-8·5m+8·2$

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

role="math" localid="1644581639804" $8·m^2-8·5m+8·2=8(m^2-5m+2)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}8(m^2-5m+2)& =& 8·m^2-8·5m+8·2\\ & =& 8m^2-40m+16\end{array}$

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