Question

If (x - 2) is a factor of 2x: 3 – *2 – px – 2.
(1) Find the value of p.
(ii) With the value of p, factorise the above expression completely.​

Answer 1

Answer:

Given expression is 2x3 – x2 – px - 2 and x – 2 is the factor.

(i) x – 2 = 0, x = 2 in expression

2(2)3 – (2)2 – p(2) – 2 = 0

16 – 4 – 2p – 2 = 0

10 – 2p = 0

p = 5

∴ 2x3 – x2 – 5x – 2 = (x – 2)(2x2 + 3x + 1)

The expression can be the written as

(2x2 + 3x + 1)(x – 2) or (2x + 1)(x + 1)(x – 2)