Q. 16 - Intermediate Algebra

Question

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

$10q^2+14q+20$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & 2(5q^2+7q+10)\end{array}$.

Step 1. Given Information

The given polynomial is $10q^2+14q+20$.

Step 2. Find the GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 10q^2=2·5·q·q \\ 14q=2·7·q \\ 20=2·2·5 \end{gathered}$$

• From the obtained factors, it is observed that the common factor is 2.
• So, the GCF of the terms of the given expression is 2.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, 2.

$2·5q^2+2·7q+2·10$

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

$2·5q^2+2·7q+2·10=2(5q^2+7q+10)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}2(5q^2+7q+10)& =& 2·5q^2+2·7q+2·10\\ & =& 10q^2+14q+20\end{array}$

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