Target Mathematics

1.4: Polynomial remainders, factor theorem and polynomial division

4PM1/2R/June/2024 — Question 4 · 11 marks

f(x)=px3+qx237x12qf(x) = px^3 + qx^2 - 37x - 12q where pp and qq are constants.
When f(x)f'(x) is divided by (x+2)(x + 2) the remainder is 33-33
Given that (x+5)(x + 5) is a factor of f(x)f(x)
(a) (i) show that p=2p = 2
(ii) find the value of qq
(6)
(b) Hence, use algebra to factorise f(x)f(x) completely.
(3)
(c) Hence solve the equation f(x)=0f(x) = 0
(2)