Question

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

$9n-63$

Short answer

The factored form is$9(n-7)$.

Step-by-step solution

Step 1. Given information

The given polynomial is$9n-63$.

Step 2. Find GCF of the terms. 

• Factor each of the terms in the given expression.

$$\begin{gathered} 9n=3·3·n \\ 63=3·3·7 \end{gathered}$$

• From the obtained factors, it is observed that the common factors are 3, 3.
• Multiply the common factors to determine the GCF.

$3·3=9$

• So, the GCF of the terms of the given expression is 9.

Step 3. Rewrite the given expression    

• Express each of the term of the given expression as a product of GCF, 9.

$9n-63=9·n-9·7$

• Use the reverse distributive property, localid="1661477142910" $ab-ac=a(b-c)$to rewrite the obtained expression.

$9(n-7)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}9(n-7)& =& 9·n-9·7\\ & =& 9n-63\end{array}$

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