Question

Find what must be subtracted from 2x⁴-4x³+4x²-4x+3 such that polynomial is divisible by x²+x+1

Answer 1

Let,

$f(x) = 2 {x}^{4} - 4 {x}^{3} + 4 {x}^{2} - 4x + 3$

The polynomial that should be subtracted from f(x) so that it is divisible by x2+x+1 = Remainder when f(x) is divided by x2 + x + 1

$= - 2x - 1$

HOPE THIS COULD HELP!!!