Q. 20

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

$8 m^{2} - 40 m + 16$

Verified

Answer

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

1Step 1. Given Information

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

2Step 2. Find the GCF of the terms

$8 m^{2} = 2 \cdot 2 \cdot 2 \cdot m \cdot m 40 m = 2 \cdot 2 \cdot 2 \cdot 5 \cdot m 16 = 2 \cdot 2 \cdot 2 \cdot 2$

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

$2 \cdot 2 \cdot 2 = 8$

3Step 3. Rewrite the given expression

$8 \cdot m^{2} - 8 \cdot 5 m + 8 \cdot 2$

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

$8 \cdot m^{2} - 8 \cdot 5 m + 8 \cdot 2 = 8 (m^{2} - 5 m + 2)$

4Step 4. Check

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

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