PSAT Math Grid-Ins Question 119: Answer and Explanation

Question: 119

If a⁴ - 2a³ + 2a² + ma + 2 has (a + 1) as a factor, what is the value of the constant m?

Correct Answer: 7

Explanation:

(7) If a + 1 is a factor, it will divide evenly into the polynomial without a remainder. You can do polynomial long division or synthetic division. We will show the steps for long division:

In order for there to be no remainder, 2 - (m - 5) must be equal to 0. Set it equal to 0 and solve for m:

2 - (m- 5) = 0

Distribute the negative sign:

2 - m + 5 = 0

Combine like terms on the right:

7 - m = 0

Adding m to both sides solves for m:

7 = m