Q. 17 - Intermediate Algebra

Question

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

$8y^3+16y^2$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & 8y^2(y+2)\end{array}$.

Step 1. Given Information

The given polynomial is $8y^3+16y^2$

Step 2. Find the GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 8y^3=2·2·2·y·y·y \\ 16y^2=2·2·2·2·y·y \end{gathered}$$

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

$2·2·2·y·y=8y^2$

• So, the GCF of the terms of the given expression is $8y^2$.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, $8y^2$.

$8y^2·y+8y^2·2$

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

$8y^2·y+8y^2·2=8y^2(y+2)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}8y^2(y+2)& =& 8y^2·y+8y^2·2\\ & =& 16y^3+16y^2\end{array}$

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