To factor the quadratic expression 5x² + 18x + 8, we need to find two numbers that multiply to the product of the leading coefficient (5) and the constant term (8), which is 40, and add up to the middle coefficient (18).
The two numbers that fulfill these conditions are 10 and 4, since 10 * 4 = 40 and 10 + 4 = 18.
Next, we can rewrite the middle term (18x) using these two numbers:
5x² + 10x + 4x + 8.
Now, we can group the terms:
(5x² + 10x) + (4x + 8).
Factoring out the greatest common factor from each group gives us:
5x(x + 2) + 4(x + 2).
Now, we can see that (x + 2) is a common factor:
(5x + 4)(x + 2).
So, the factored form of the expression 5x² + 18x + 8 is:
(5x + 4)(x + 2)