To factor the quadratic expression 2x² + 7x + 6, we look for two numbers that multiply to the product of the leading coefficient (2) and the constant term (6), which is 12, and add up to the middle coefficient (7).
First, we identify the pairs of factors of 12:
- 1 and 12
- 2 and 6
- 3 and 4
Among these pairs, 3 and 4 add up to 7. So, we can rewrite the middle term (7x) using these numbers:
2x² + 3x + 4x + 6
Next, we group the terms:
(2x² + 3x) + (4x + 6)
Now, we factor out the common terms in each group:
x(2x + 3) + 2(2x + 3)
We can see that (2x + 3) is a common factor:
(2x + 3)(x + 2)
Thus, the factored form of the expression 2x² + 7x + 6 is:
(2x + 3)(x + 2)