Question

Select the two binomials that are factors of this trinomial.
x^2+8x+12

0x+6

0x+2

0x-2

0x+8

Answer 1

To factor the trinomial \(x^2 + 8x + 12\), we can look for two binomials of the form \((x + a)(x + b)\) where \(a\) and \(b\) are numbers that multiply to the constant term (12) and add up to the linear coefficient (8).

The factors of 12 that add up to 8 are 6 and 2. Thus, we can write:

\[
x^2 + 8x + 12 = (x + 6)(x + 2)
\]

The two binomials that are factors of the trinomial \(x^2 + 8x + 12\) are:

1. \(x + 6\) (this corresponds to \(0x + 6\))
2. \(x + 2\) (this corresponds to \(0x + 2\))

So the correct selections from your options are:

- \(0x + 6\)
- \(0x + 2\)