Question

what must be added the polynomial f(x)=x4+2x3-2x2+x-1 so that the resulting polynomial is exactly divisibleby by x2+2x-3 ​

Answer 1

f(x)= x4 + 2x3 - 2x2 + x - 1

Let g(x) = x2 + 2x - 3

on dividing f(x) by g(x)

Remainder = 2 - x

Hence, -(2-x) = x - 2 must be added.