Find the remainder when 2x² – 3x + 5 is divided by 2x – 3. Does it exactly divide the polynomial? State reason.

Let p(x) = 2x² – 3x + 5

As we know by Remainder Theorem,

If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)

⇒ Remainder of p(x) when divided by 2x – 3 is

⇒ Remainder of 2x² – 3x + 5 when divided by 2x – 3 is

As on dividing the given polynomial by 2x – 3, we get a non–zero remainder, therefore, 2x – 3 does not complete divide the polynomial.

∴ It is not a factor.