Question

Which of the following is a factor of 2y^2 + 12y - 54?

a) (y - 9)
b) (y - 3)
c) (2y + 6)
d) (y + 6)

Answer 1

Option (b) (y - 3) is the factor of the polynomial 2y^2 + 12y - 54, as it makes the value of the polynomial equal to zero.

Step-by-step explanation:

To determine which of the given options is a factor of the polynomial 2y2 + 12y - 54, we can use either polynomial division or the factor theorem. The factor theorem states that if (y - c) is a factor of the polynomial, then the polynomial will be equal to zero when y = c.

Let's test each option by substituting y with the value that would make the binomial zero:

1. For (y - 9), substitute y = 9: 2(9)2 + 12(9) - 54 = 162 + 108 - 54 = 216, which is not zero, so it is not a factor.
2. For (y - 3), substitute y = 3: 2(3)2 + 12(3) - 54 = 18 + 36 - 54 = 0, which is zero, so (y - 3) is a factor.
3. For (2y + 6), we can see right away it cannot be a factor as the leading coefficient of the polynomial is 2. A factor in such a form would mean the polynomial is divisible by 2, leaving us with a term that does not have 2 as a coefficient, which is not the case here.
4. For (y + 6), substitute y = -6: 2(-6)2 + 12(-6) - 54 = 72 - 72 - 54, which is not zero, so it is not a factor.

Therefore, the correct answer is (b) (y - 3), which is a factor of 2y2 + 12y - 54.