Question

# What must be added to the polynomial f(x)=x+ +2x2_2x2+x-so that the resulting polynomial is exactly divisible by x2 + 2x - 3?

Solution

The given polynomial is f(x) = x4 + 2x3 - 2x2 + x - 1. To
make this polynomial exactly divisible by
x2 + 2x - 3, let us add p then x4 + 2x3 - 2x2 + x-1+p is
exactly divisible by x2 + 2x-3.
x
x + 2x - 3) x + 2x - 2x + x-1+p
4 3 2
x + 2x - 3x
- - +
x+x-1+p
For remainder to be zero, x2 + 2x -3 = x2 + x-1+p
So,p=x-2,
So, X-2 to be added to make the polynomial divisible by
x2 + 2x-3.