To factor the quadratic expression 5x² + 28x + 15, we can use the method of grouping or look for two numbers that will help us break it down.
First, identify the coefficients: a = 5, b = 28, and c = 15. We need two numbers that multiply to a*c = 5*15 = 75 and add up to b = 28.
The two numbers that meet these criteria are 25 and 3 because 25 * 3 = 75 and 25 + 3 = 28.
Now, we can rewrite the middle term (28x) using these numbers:
5x² + 25x + 3x + 15
Next, we group the terms:
(5x² + 25x) + (3x + 15)
Factor out the common factors in each group:
5x(x + 5) + 3(x + 5)
Now, we can see that (x + 5) is common in both terms:
(5x + 3)(x + 5)
So, the factored form of the expression 5x² + 28x + 15 is:
(5x + 3)(x + 5)