Question

Without actual division prove that the 4 +23 - 22 + 2x – 3 is exactly divisible by 2 +2x -3

Answer 1

p(x)= 4+23-22+2x-3

g(x)= 2+2x-3

Using Remainder Theorem,

g(x)=0

2+2x-3=0

2x-1=0

2x=1

x=½.

Putting x= 1/2! in p(x)= 4+23-22+2x-3

p(1/2)= 2+23-22+2×1/2-3

2+1+1-3

3-2

-1.