Find the polynomial of least degree that should be subtracted from `p(x)=x^3-2x^2+3x+4` so that it is exactly divisible by `g(x)=x^2-3x+1`

What must be subtracted from (x^(3)+5x^(2)+5x+8) so that the resulting polynomial Is excatly divisible by (x^(2)+3x-2) ?

What should be added to x^(4)-1 so that it is exactly divisible by 2x^(2)+2x+1

What must be added to f(x) = x^(4) + 2x^(3) - 2x^(2) + x- 1 so that the polynomial is exactly divisible by g(x) = x^(2) +2x - 3 ?

We must be added to 2x^(3)+3x^(2)-22x+12 so that the result is exactly divisible by 2x^(2)+5x-14

Find zero of the polynomial p (x) = 3x +1

What must be added to the polynomial P(x)= x^(4)+2x^(3)-2x^(2)+x-1 So that the resulting polynomial is excatly divisible by x^(2)+x-3

Without actual division, show that f(x) = 2x^(4) - 6x^(3) + 3x^(2) + 3x - 2 is exactly divisible by x^(2)- 3x + 2 .

What must be (a) subtracted from (b) added to f(x) = 8x^(4) + 14 x^(3) - 2x^(2) + 7 x - 8 so that resulting polynomial is exactly divisible by 4x^(2) + 3x - 2 ?

What real number should to subtracted from the polynomial 3x^(3) + 10x^(2) - 14 x + 9 so that (3x - 2) divides it exactly ?

What must be added to f(x) = x^(4) + 2x^(3) - 2x^(2) + x- 1 so that the resulting polynomial is a multiple of x^(2) + 2x - 3 ?