Question

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

Answer 1

x - 2

By division Algorithm we have,

From above relation we got that if we add -r(x) to f(x) then resulting polynomial is divisible by g(x).

Now find the remainder when f(x) is divisible by g(x),

r(x) = - x + 2

Therefore,

- r(x) = x - 2 has to be added so that resulting polynomial is divisible by g(x).