Target Mathematics

1.15: where is an integer.

4PM1/1/January/2017 — Question 2 · 9 marks

f(x)=2x33px2+x+4pf(x)=2x^3-3px^2+x+4p where pp is an integer.
Given that (x4)(x-4) is a factor of f(x)f(x)
(a) show that the value of pp is 3 (2)
Using this value of pp,
(b) find the remainder when f(x)f(x) is divided by (x+2)(x+2) (2)
(c) factorise f(x)f(x) completely (3)
(d) solve the equation 2x33px2+x+4p=02x^3-3px^2+x+4p=0 (2)