1.8: Cubic with a repeated factor found without a calculator

0606/12/O/N/16 — Question 9 · 9 marks

Do not use a calculator in this question.

The polynomial

p(x)

ax^{3} - 4x^{2} + bx + 18

. It is given that

p(x)

and

p'(x)

are both divisible by

2x - 3

(i)

Show that

a = 4

and find the value of

b

[4]

(ii)

Using the values of

a

and

b

from part (i), factorise

p(x)

completely.

[2]

(iii)

Hence find the values of

x

for which

p(x) = x + 2

[3]