3.15: Factor and remainder; three linear factors

0606/12/O/N/21 — Question 6 · 9 marks

Do not use a calculator in this question.

The polynomial p(x)=10x3+ax2−10x+bp(x) = 10x^{3} + ax^{2} - 10x + b, where aa and bb are integers, is divisible by 2x+12x + 1.
When p(x)p(x) is divided by x+1x + 1, the remainder is −24-24.
(a)
Find the value of aa and of bb.
[4]
(b)
Find an expression for p(x)p(x) as the product of three linear factors.
[4]
(c)
Write down the remainder when p(x)p(x) is divided by xx.
[1]