perplexus.info :: Just Math : Integer Identification

Integer Identification (Posted on 2015-02-14)

Find all integer values of p such that x³ + 2x + p divides:
x¹² - x¹¹ + 3x¹⁰ + 11x³ - x² + 23x + 30.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (3 votes)

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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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