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Polynomial Factors 
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#1
Oct1107, 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^316x+b, find the values of a and b." Anyone have any ideas? 


#2
Oct1107, 11:59 PM

P: 461

We have that there is a c such that (x^2+ax+1)(2x+c)=2x^316x+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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