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Homework Statement
The division of a polynomial f(x) by (x – 1)(x – 2) has remainder x + 1. If the remainder of the division of f(x) by (x – 1) and (x – 2) are, respectively, a and b. Then what is a^2 + b^2?
Homework Equations
I guess the remainder theorem could be useful here.
The Attempt at a Solution
f(x) = q(x)(x – 1) + a; where q(x) is the quotient of the division of f(x) by (x – 1).
f(x) = p(x)(x – 2) + b; where p(x) is the quotient of the division of f(x) by (x – 2).
q(x)(x – 1) + a = p(x)(x – 2) + b
I don't know how to move forward using the fact the remainder of the division of f(x) by (x – 1)(x – 2).