Given that x-1 and x+2 are factors of f(x)= x^3 + px + q where p and q are integers, find p and q.

How do i start in find p and q????

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- January 9th 2012, 06:23 PMRyan12factor theorm
Given that x-1 and x+2 are factors of f(x)= x^3 + px + q where p and q are integers, find p and q.

How do i start in find p and q???? - January 9th 2012, 06:25 PMQuackyRe: factor theorm
If is a factor, then

- January 9th 2012, 06:32 PMRyan12Re: factor theorm
so wait if i use x-1 then where x is, it would be replaced by 1,

F(1) = 1^3 + p(1) + q

and i was just end up where i started, so how to advance on this questions , and thanks - January 9th 2012, 06:37 PMQuackyRe: factor theorm

This gives you one equation in and . Now find another using the other factor. - January 9th 2012, 07:02 PMRyan12Re: factor theorm
then i simultaneously solve right???

thanks alot your help greatly appreciated, - January 9th 2012, 07:05 PMMarkFLRe: factor theorm
Another method:

We know k is real as complex roots come in conjugate pairs.

Now equate coefficients.