Find the number a such that x-1 is a factor of x^3+ax^2-x+8
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Find the number a such that x-1 is a factor of x^3+ax^2-x+8
Use the polynomial remainder theorem.
Also, you could use Vieta's theorem.
When you have:, you know that:
... whereare roots of
.
So when you haveand you know that 1 is root (
), you can write three equations:
... so you have 3 equations with three unknowns, and you can solve for.
Well, if you really want to do it the hard way! Personally I would prefer to evaluate the polynomial at x= 1.
Thanks guys that was a huge help!!