Question

Which two binomials are factors of the trinomial x^2 + 8x + 12?

A. x-2
B. x+2
C. x+8
D. x+6

Answer 1

The two binomials that are factors of the trinomial x^2 + 8x + 12 are (x + 2) and (x + 6), found by identifying two numbers that add to 8 and multiply to 12.

Step-by-step explanation:

The question asks which two binomials are factors of the trinomial x^2 + 8x + 12. To factor this trinomial, we look for two numbers that both add up to 8 (the coefficient of the middle term) and multiply to 12 (the constant term). The two numbers that meet these criteria are 2 and 6. Therefore, the two binomial factors of the trinomial x^2 + 8x + 12 are:

• (x + 2)
• (x + 6)

We can verify this by using the FOIL method to check if (x + 2) and (x + 6) when multiplied give the original trinomial:

(x + 2)(x + 6) = x^2 + 6x + 2x + 12 = x^2 + 8x + 12.