Q. 18

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

$12 x^{3} - 10 x$

Verified

Answer

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

1Step 1. Given Information

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

2Step 2. Find the GCF of the terms

$12 x^{3} = 2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot x 10 x = 2 \cdot 5 \cdot x$

$2 \cdot x = 2 x$

3Step 3. Rewrite the given expression

$2 x \cdot 6 x^{2} - 2 x \cdot 5$

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

$2 x \cdot 6 x^{2} - 2 x \cdot 5 = 2 x (6 x^{2} - 5)$

4Step 4. Check

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

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