# Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 22, 2011"

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+ | If there is only one integer root, if it is in the form <math>x - y</math>, and <math>y</math> is a constant, then <math>y</math> must be a factor of <math>25</math>, the polynomial's constant term, because of the Factor Theorem. <math>-1</math> and <math>1</math> are not zeros. Going up from there, we see that <math>5</math> is a zero, so our answer is <math>5</math>. | ||

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+ | [[Category: Intermediate Algebra Problems]] |

## Latest revision as of 14:41, 22 July 2011

## Problem

AoPSWiki:Problem of the Day/July 22, 2011

## Solution

If there is only one integer root, if it is in the form , and is a constant, then must be a factor of , the polynomial's constant term, because of the Factor Theorem. and are not zeros. Going up from there, we see that is a zero, so our answer is .