How do you factor 6x^2 + 13x + 6?

To factor the quadratic expression 6x² + 13x + 6, follow these steps:

Multiply the leading coefficient and the constant term:

The leading coefficient is 6 (from 6x²).
The constant term is 6.
Multiply them: 6 * 6 = 36.
Find two numbers that multiply to give 36 and add up to the middle coefficient (13):

We need to find two numbers that multiply to 36 and add to 13.
The numbers 9 and 4 work because 9 * 4 = 36 and 9 + 4 = 13.
Rewrite the middle term using the two numbers:

Break the middle term 13x into 9x and 4x: 6x² + 9x + 4x + 6.
Factor by grouping:

Group the terms in pairs: (6x² + 9x) and (4x + 6).
Factor each group:
From 6x² + 9x, factor out 3x: 3x(2x + 3).
From 4x + 6, factor out 2: 2(2x + 3).
Factor out the common binomial:

The common binomial factor is (2x + 3).
Factor it out: (3x + 2)(2x + 3).
Thus, the factorization of 6x² + 13x + 6 is: (3x + 2)(2x + 3).