Question

what must be subtracted from f(x) =4x^4 +2x^3 - 2x^2 +x-1, so that the resulting polynimial is divisible by g(x)=x^2 +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).Read more on Sarthaks.com - https://www.sarthaks.com/37230/what-must-be-added-to-4x-4-2x-3-2x-2-x-1-so-that-the-resulting-polynomial-is-divisible-by-g-x-x-2-2x