Question

The polynomials ax³- 3x² + 4 and 2x³ - 5x + a when divided by x -2 leave the remainder p & q respectively. If p -2q = 4 find the value of a.

Answer 1

p(x)= ax^3- 3x^2+4
x-2=0
x=2
p(2)=a(2)^3-3(2)^2+4
=8a-12+4=8a-8=p

f(x)= 2x^3-5x+a
f(2)= 2(2)^3-5(2)+a
=16-10+a
=6+a=q

p-2q=4
8a-8-6-a=4
7a-14=4
7a=18

a=18/7

Answer 2

x=2 a{2}3-3{2}2+4=8a-8 _p

2{2]3-5{2}+a =6+a _q

8a-8-2(6+a) =4

8a--8-12-2a=4

8a-20-2a=4

8a-2a=4+20

6a=24

a=24/6

a=4