MathDB

2009 Algebra #4 - LCM and GCD of Polynomials

Source:

January 2, 2012

number theoryleast common multiplegreatest common divisoralgebrapolynomialquadratics

Problem Statement

Suppose

a

b

and

c

are integers such that the greatest common divisor of

x^2+ax+b

and

x^2+bx+c

x+1

(in the set of polynomials in

x

with integer coefficients), and the least common multiple of

x^2+ax+b

and

x^2+bx+c

x^3-4x^2+x+6

. Find

a+b+c