Target Mathematics

1.18: When $f(x)$ is divided by $(x-2)$ the remainder is $-20$

4PM1/2/January/2016 — Question 10 · 12 marks

f(x)=2x3−px2−13x−qf(x)=2x^3-px^2-13x-q
When f(x)f(x) is divided by (x−2)(x-2) the remainder is −20-20. Given that (x−3)(x-3) is a factor of f(x)f(x)
(a) find the value of pp and the value of qq. (7)
(b) Hence use algebra to solve the equation f(x)=0f(x)=0. (5)