The problem asks us to factor the quadratic expression $y^2 + 2y - 8$, if possible. If the expression cannot be factored, we are to state that the polynomial is prime.

1. Problem Description

The problem asks us to factor the quadratic expression $y^2 + 2y - 8$, if possible. If the expression cannot be factored, we are to state that the polynomial is prime.

2. Solution Steps

We are looking to factor the quadratic expression $y^2 + 2y - 8$.

We are looking for two numbers that multiply to -8 and add to

2. The factors of -8 are:

1 and -8

-1 and 8

2 and -4

-2 and 4

The pair of factors that adds to 2 is -2 and

4. Therefore, the factored form is $(y - 2)(y + 4)$.

We can check our answer by expanding the factored form:

$(y - 2)(y + 4) = y(y + 4) - 2(y + 4) = y^2 + 4y - 2y - 8 = y^2 + 2y - 8$.

The factored expression is correct.

3. Final Answer

A. $y^2 + 2y - 8 = (y-2)(y+4)$