Question

what linear polynomial should be added in the polynomial x cube + 2 x square - 9 X + 1 so that it is completely divisible by X + 4​

Answer 1

P(x) = x^3 + 2x^2 - 9x +1

By Remainder theoram

If P(x) is divided by (x+4)

P(-4) = (-4)^3 + 2(-4)^2 - 9(-4) + 1

Remainder = - 64 + 32 + 36 +1

Remainder = 5

The number to be added to P(x) = 5

thank you