Question

Frank is trying to factor y^2+6y-27 . He has determined that one factor is (y + 9). What is the other factor? A. y – 27 B. y – 6 C. y – 9 D. y – 3

Answer 1

The other factor is (y - 3).  If you multiply the two terms together, you will end up with $y^2+6y-27$:

$(y - 3)(y + 9) \\ y^{2} +9y-3y-27 \\ y^2+6y-27$

Answer 2

Identify b and c in the equation:

b = 6
c = -27

Two factors must add to b, and two factors must multiply to c.

We know that one of the factors is 9, so we can set up the following equations to solve for the missing factor:

$9 + y = 6$

Subtract 9 from both sides:

$y = -3$

-

$9y = -27$

Divide both sides by 9 to get y by itself:

$y = -3$

The other factor is D. (y - 3).