Question

Select the two binomials that are factors if this trinomial
x^2+6x+8

x-4
x+4
x+2
x+8

Answer 1

To factor the trinomial \( x^2 + 6x + 8 \), we need to find two binomials of the form \( (x + p)(x + q) \) such that:

1. \( p + q = 6 \) (the coefficient of the \( x \) term).
2. \( p \cdot q = 8 \) (the constant term).

Examining the possible pairs of factors of 8:

- \( (1, 8) \): \( 1 + 8 = 9 \)
- \( (2, 4) \): \( 2 + 4 = 6 \)
- \( (4, 2) \): \( 4 + 2 = 6 \)
- \( (-1, -8) \): \( -1 + -8 = -9 \)
- \( (-2, -4) \): \( -2 + -4 = -6 \)

The pair that works is \( (2, 4) \).

Thus, the factors of the trinomial \( x^2 + 6x + 8 \) are \( (x + 2)(x + 4) \).

Among the options you provided, the correct binomials that are factors are:

- \( x + 4 \)
- \( x + 2 \)

So the answer is \( x + 4 \) and \( x + 2 \).