Q. 6.10 - Intermediate Algebra

Question

Factor: $-7a^3+21a^2-14a$

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & -7a(a^2-3a+2)\end{array}$.

Step 1. Given Information

The given expression is $-7a^3+21a^2-14a$.

Step 2. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, $-7a$.

$-7a·a^2-(-7a)·3a+(-7a)·2$

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

$-7a·a^2-(-7a)·3a+(-7a)·2=-7a(a^2-3a+2)$

Steck 3. Check

• Multiply the obtained factors.

$\begin{array}{rcl}-7a(a^2-3a+2)& =& -7a·a^2-(-7a)·3a+(-7a)·2\\ & =& -7a^3+21a^2-14a\end{array}$

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