Q. 13 - Intermediate Algebra

Question

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

$3x^2+6x-9$

Step-by-Step Solution

Answer

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

Step 1. Given Information

The polynomial is $3x^2+6x-9$.

Step 2. Find the GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 3x^2=3·x·x \\ 6x=3·2·x \\ 9=3·3 \end{gathered}$$

• From the obtained factors, it is observed that the common factor is 3.
• So, the GCF of the terms of the given expression is 3.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, 3.

$3·x^2+3·2x-3·3=3(x^2+2x-3)$

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

$3·x^2+3·2x-3·3=3(x^2+2x-3)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}3(x^2+2x-3)& =& 3·x^2+3·2x-3·3\\ & =& 3x^2+6x-9\end{array}$

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