Question

what must be subtracted from the polynomial p(x)=x⁴+2x³-4x²-6x-3 so that it is exactly divisible by x²+x-1​

Answer 1

Answer:

x²+x-1)x⁴+2x³-4x²-6x-3(x²+x-2

x⁴+1x³-1x²

(-) (-) (+)

_______________

1x³-3x²-6x

1x³+1x²-1x

(-) (-) (+)

_________________

-2x²-5x-3

-2x²-2x+2

(+) (+) (-)

__________________

-3x-5

___________________

therefore, -3x-5 must be subtracted from the polynomial

x⁴+2x³-4x²-6x-3 so that it is exactly divisible by x²+x-1