Q. 10 - Intermediate Algebra

Question

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

$14p+35$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & 7(2p+5)\end{array}$.

Step 1. Given Information

The given polynomial is $14p+35$.

Step 2. Find GCF of the terms.

• Factor each of the terms in the given expression.

$$\begin{gathered} 14p=2·7·p \\ 35=5·7 \end{gathered}$$

• From the obtained factors, it is observed that the common factor is 7.
• So, the GCF of the terms of the given expression is 7.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, 7.

$14p+35=7·2p+7·5$

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

$7·2p+7·5=7(2p+5)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}7(2p+5)& =& 7·2p+7·5\\ & =& 14p+35\end{array}$

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