To factor the quadratic expression x² + 5x + 6, we need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the x term).
Looking at the pairs of factors of 6, we have:
- 1 and 6
- 2 and 3
The pair that adds up to 5 is 2 and 3.
So we can rewrite the expression as:
x² + 2x + 3x + 6
Now, we can group the terms:
(x² + 2x) + (3x + 6)
Factoring out the common terms in each group gives us:
x(x + 2) + 3(x + 2)
Now, we can factor out the common binomial (x + 2):
(x + 2)(x + 3)
Therefore, the factored form of x² + 5x + 6 is:
(x + 2)(x + 3)