Q. 12 - Intermediate Algebra

Question

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

$45b-18$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & 9(5b-2)\end{array}$.

Step 1. Given Information

The given polynomial is $45b-18$.

Step 2. Find the GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 45b=5·3·3·b \\ 18=2·3·3 \end{gathered}$$

• From the obtained factors, it is observed that the common factors are 3, 3.
• Multiply the common factors to determine the GCF.

$3·3=9$

• So, the GCF of the terms of the given expression is 9.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, 9.

$9·5b-9·2$

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

$9(5b-2)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}9(5b-2)& =& 9·5b-9·2\\ & =& 45b-18\end{array}$

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