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Integer Identification (Posted on 2015-02-14) Difficulty: 3 of 5
Find all integer values of p such that x3 + 2x + p divides:
x12 - x11 + 3x10 + 11x3 - x2 + 23x + 30.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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Solution Doing the work (spoiler) | Comment 2 of 3 |
Well, once you know that p = 3 or p = -2, the factoring is fairly easy.

x12 - x11 + 3x10 + 11x3 - x2 + 23x + 30 = 

(x3 + 2x + 3) *

(x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x + 10)

But  x3 + 2x -2 does not divide evenly into the expression

So, the only solution is p = 3

Edited on February 14, 2015, 7:55 pm
  Posted by Steve Herman on 2015-02-14 10:03:52

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