Find the number a such that x-1 is a factor of x^3+ax^2-x+8

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- Nov 6th 2012, 10:22 AMskweres1Algebra II
Find the number a such that x-1 is a factor of x^3+ax^2-x+8

- Nov 6th 2012, 11:04 AMemakarovRe: Algebra II
Use the polynomial remainder theorem.

- Nov 6th 2012, 11:14 AMPaulAdrienMauriceDiracRe: Algebra II
Also, you could use Vieta's theorem.

When you have: , you know that:

... where are roots of .

So when you have and you know that 1 is root ( ), you can write three equations:

... so you have 3 equations with three unknowns, and you can solve for . - Nov 6th 2012, 12:44 PMHallsofIvyRe: Algebra II
Well, if you

**really**want to do it the**hard**way! Personally I would prefer to evaluate the polynomial at x= 1. - Nov 6th 2012, 01:17 PMskweres1Re: Algebra II
Thanks guys that was a huge help!!