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We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is factor

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by Max@Math Revolution » Tue Feb 18, 2020 1:55 am
[GMAT math practice question]

We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is factored into (x + a)(x + b) where a and b are integers. How many different values of n satisfy the polynomial x^2 + 4x – n?

A. 5
B. 6
C. 7
D. 8
E. 9
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Re: We have a polynomial x^2 + 4x - n for an integer n between 1 and 100, inclusive. The polynomial x^2 + 4x - n is fac

by Max@Math Revolution » Thu Feb 20, 2020 12:51 am
=>

We can assume a < b without loss of generality.
Since we have a + b = 4 and ab = -n, we have the following pairs of (a, b).
(-1, 5), (-2, 6), (-3, 7), (-4, 8), (-5, 9), (-6, 10), (-7, 11), (-8, 12)
Then, the possible values of n are 5, 12, 21, 32, 45, 60, 77 and 96.
We have 8 possible values of n.

Therefore, the answer is D.
Answer: D
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