Find a and b in order that `x^3 - 6x^2 + ax + b` may be exactly divisible by `x^2 - 3x + 2`

Find the relation between a and b so that (2x^4 - 7x^3 + ax + b) may be divisible by (x - 3) .

Find the relation between a and b so that 2x^4 - 7x^3 + ax + b may be divisible by x - 3.

If x^(3) + 6x^(2) + kx + 6 is exactly divisible by ( x + 2) , then k = ?

Prove that (x^3-3x^2-13x+15) is exactly divisible by x^2+2x-3

Without actual division prove that 2x^4- 6x^3 +3x^2+3x-2 is exactly divisible by x^2- 3x +2 is

Find the values of a and b for which ax^(3)-11x^(2)+ax+b is exactly divisible by x^(2)-4x-5

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