Target Mathematics

1.17: Polynomial remainders, polynomial division and polynomial roots

4PM1/1/January/2015 — Question 9 · 12 marks

f(x)=2x3+ax2+bx+15f(x)=2x^3+ax^2+bx+15
where aa and bb are constants.
The remainder when f(x)f(x) is divided by x−1x-1 is −12-12. The remainder when f(x)f(x) is divided by x+1x+1 is 48.
(a) Find the value of aa and the value of bb. (6)
(b) Show that f ⁣(12)=0f\!\left(\dfrac12\right)=0. (1)
(c) Express f(x)f(x) as a product of linear factors. (4)
(d) Hence solve f(x)=0f(x)=0. (1)