Q. 9 - Intermediate Algebra

Question

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

$6m+9$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & 3(2m+3)\end{array}$.

Step 1. Given Information

The given polynomial is $6m+9$.

Step 2. Find GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 6m=2·3·m \\ 9=3·3 \end{gathered}$$

• From the obtained factors, it is observed that the common factor is 3 .
• So, the GCF of the terms of the given expression is 3.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, 3.

$6m+9=3·2m+3·3$

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

$3·2m+3·3=3(2m+3)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}3(2m+3)& =& 3·2m+3·3\\ & =& 6m+9\end{array}$

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