Question

How do I factor the expression 24x + 18?

Answer 1

To factor the expression \( 24x + 18 \), you first need to find the greatest common factor (GCF) of the coefficients 24 and 18.

1. **Find the GCF**:
- The factors of 24 are \( 1, 2, 3, 4, 6, 8, 12, 24 \).
- The factors of 18 are \( 1, 2, 3, 6, 9, 18 \).
- The common factors are \( 1, 2, 3, 6 \). The greatest of these is \( 6 \).

2. **Factor out the GCF**:
- Divide each term in the expression by the GCF (6):
\[
24x \div 6 = 4x
\]
\[
18 \div 6 = 3
\]
- Now, write the expression with the GCF factored out:
\[
24x + 18 = 6(4x + 3)
\]

So, the factored form of the expression \( 24x + 18 \) is:
\[
\boxed{6(4x + 3)}
\]