Question

find the remainder when 2x^2-3x+5 is divided by 2x-3. Does it exactly divide the polynomial? state reason.

Answer 1

There are two methods of verifying if it actually divides the polynomial or not:

Firstly by simple division and secondly by putting the value of x obtained from the second equation in the polynomial.

Let 2x-3 = 0

then, x = 3/2 = 1.5

Now, we need to put this value in the polynomial: 2x^2-3x+5 = (2 x 9/4) - 9/2 + 5 = 9/2 -9/2 + 5 = 5 which is not equals to zero. That means 2x - 3 doesn't divides the polynomial.