Skill: 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 $12x+18$

1. 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 $6$.

2. Divide each term by $6$.

$$12x\div 6=2x$$ $$18\div 6=3$$

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

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

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

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

So, the factored form is

$$\boxed{6(2x+3)}$$