Factor expressions using a common factor

Factoring an expression with a common factor means rewriting a sum or difference as a product by identifying a factor shared by every term, such as $6x+9=3(2x+3)$ , using the distributive property in reverse. The factored and expanded forms are equivalent, and expansion verifies the result; the work is limited to simple numerical factors and shared variables in basic terms, not quadratic factoring or other advanced polynomial methods.

Detailed Explanation: Factor expressions using a common factor

To factor an expression, look for a factor that appears in every term. Then use the distributive property in reverse:

ab+ac=a(b+c)

Example: Factor $12x+18$

Find the greatest common factor of the terms.
The greatest common factor of $12$ and $18$ is $6$ . There is no variable in both terms, so the common factor is $6$ .
Divide each term by $6$ .

12x\div 6=2x

18\div 6=3

Write the common factor outside parentheses.
Put the results inside the parentheses:

12x+18=6(2x+3)

Check by expanding.
Multiply $6$ by each term inside the parentheses:

6(2x+3)=12x+18

So, the factored form is

\boxed{6(2x+3)}

Learn by doing: Factor expressions using a common factor

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