How to proceed in this problem? I divided n^3+4n^2+4n−14 by n^2+2n+2 and equated the remainder to zero . I got n=5 as answer but the answer is wrong.

tikaj1x

tikaj1x

Answered question

2022-10-16

What is the sum of all integers n such that n 2 + 2 n + 2 divides n 3 + 4 n 2 + 4 n 14?
How to proceed in this problem? I divided n 3 + 4 n 2 + 4 n 14 by n 2 + 2 n + 2 and equated the remainder to zero . I got n = 5 as answer but the answer is wrong.

Answer & Explanation

Mohammad Cantrell

Mohammad Cantrell

Beginner2022-10-17Added 10 answers

It must help:
n 3 + 4 n 2 + 4 n 14 n 2 + 2 n + 2 = n + 2 2 n + 18 n 2 + 2 n + 2 .
Thus, or
| 2 n + 18 n 2 + 2 n + 2 | 1 ,
which gives
4 n 4
I got n { 0 , 1 , 4 , 2 , 4 }
Also, we have n = 9

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