Question

Factor:$20x^3-10x^2+14x$.

Short answer

The required factor is$2x\left(10x^2-5x+7\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$20x^3-10x^2+14x$

Step 2. Find the GCF.

Find the GCF of $20x^3,10x^2,\mathrm{and}14x$,

localid="1647709199030" $$\begin{gathered} 20x^3=2·2·5·x·x·x \\ 10x^2=2·5·x·x \\ 14x=2·7·x \end{gathered}$$

GCF is:

$$\begin{gathered} =2·x \\ =2x \end{gathered}$$

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$2x·10x^2-2x·5x+2x·7$

Factor the GCF,

$2x\left(10x^2-5x+7\right)$