polynomials equation

Question

the polynomials f(x) = x⁴-2x³-px²+q is divisible by (x-2)².find the values p and q.hence,solve the equation.

Answer 1

quotient = x^2 +2x +2 or if you want to factor it further (x+1+i)(x+1-i)

just use long division to calculate q= 8, p=2

divide x^2 -4x +4 into x^4 -2x^3 -2x + 8