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Polynomial Factors

by evanbirch
Tags: factors, polynomial
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evanbirch
#1
Oct11-07, 10:44 PM
P: 1
This problem came up on a math contest the other day and I drew a blank - now it's bugging me.

"If the polynomial P(x)=x^2+ax+1 is a factor of T(x)=2x^3-16x+b, find the values of a and b."

Anyone have any ideas?
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DeadWolfe
#2
Oct11-07, 11:59 PM
P: 461
We have that there is a c such that (x^2+ax+1)(2x+c)=2x^3-16x+b. Thus comparing coefficients gives us:

c+2a=0
2+ac=-16
b=c

Solving this yields

a=3 or -3, and thus
b=-6 or 6


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