Question

What must be added to f(x) = 4x⁴ + 2x³ – 2x² + x – 1 so that the resulting polynomial is divisible by g(x) = x² + 2x – 3?

Answer 1

By division algorithm, we have

Clearly, RHS is divisible by g(x). Therefore, LHS is also divisible by g(x). Thus, if we add – r(x) to f(x) then the resulting polynomial is divisible by g(x). Let us now find the remainder when f(x) is divided by g(x).

Hence, we should add –r(x) = 61x – 65 to f(x) so that the resulting polynomial is divisible by g (x).