3.9: Division form, then factorise p(x)−5p(x) - 5

0606/11/M/J/24 — Question 2 · 6 marks

Do not use a calculator in this question.

The polynomial pp is such that p(x)=6x3−35x2+34x+45p(x) = 6x^{3} - 35x^{2} + 34x + 45.
(a)
Find p(x)p(x) in the form (2x−5)q(x)+r(2x - 5)q(x) + r, where q(x)q(x) is a polynomial and rr is a constant.
[3]
(b)
Hence write the expression p(x)−5p(x) - 5 as a product of linear factors.
[2]
(c)
Hence write down the solutions of the equation p(x)=5p(x) = 5.
[1]