To factor the quadratic expression 3x² + 10x + 8, we need to find two binomials that multiply together to give us this expression.
We start with the standard form of a quadratic, ax² + bx + c, where:
- a = 3
- b = 10
- c = 8
Next, we need to find two numbers that multiply to a * c = 3 * 8 = 24 and add up to b = 10.
The numbers that meet these criteria are 6 and 4 because:
- 6 * 4 = 24
- 6 + 4 = 10
Now we can rewrite the middle term (10x) using 6 and 4:
3x² + 6x + 4x + 8
Next, we group the terms to factor by grouping:
- (3x² + 6x) + (4x + 8)
Factoring out common factors from each group gives us:
- 3x(x + 2) + 4(x + 2)
Now, we can factor out the common binomial factor, which is (x + 2):
(x + 2)(3x + 4)
Thus, the factorization of 3x² + 10x + 8 is: