Thread: factor 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????

If is a factor, then

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

This gives you one equation in and . Now find another using the other factor.

then i simultaneously solve right???
thanks alot your help greatly appreciated,

Another method:



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







Now equate coefficients.