The factorization of the quadratic expression 8x² + 13x + 6 can be found using several methods, such as factoring by grouping or applying the quadratic formula to find the roots. However, we will focus on factoring by grouping for simplicity.
First, we need to multiply the leading coefficient (8) by the constant term (6), which gives us 48. Now, we look for two numbers that multiply to 48 and add up to the middle coefficient (13). The numbers that meet this criterion are 3 and 16.
Next, we can rewrite the middle term (13x) using these two numbers:
8x² + 3x + 16x + 6
Now, we can group the terms:
(8x² + 3x) + (16x + 6)
Factor out the greatest common factor from each group:
x(8x + 3) + 2(8x + 3)
Now, we can see that (8x + 3) is a common factor:
(8x + 3)(x + 2)
Thus, the factorization of the quadratic expression 8x² + 13x + 6 is:
(8x + 3)(x + 2)