Question

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

$12x^3-10x$

Short answer

The factored form is$\begin{array}{rcl}& & 2x(6x^2-5)\end{array}$.

Step-by-step solution

Step 1. Given Information

The given polynomial is$12x^3-10x$.

Step 2. Find the GCF of the terms  

• Factor each of the terms in the given expression.

$$\begin{gathered} 12x^3=2·2·3·x·x·x \\ 10x=2·5·x \end{gathered}$$

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

$2·x=2x$

• So, the GCF of the terms of the given expression is $2x$.

Step 3. Rewrite the given expression   

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

$2x·6x^2-2x·5$

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

role="math" localid="1644580826454" $2x·6x^2-2x·5=2x(6x^2-5)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}2x(6x^2-5)& =& 2x·6x^2-2x·5\\ & =& 12x^3-10x\end{array}$

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