Question

 What number must be subtracted from 2x² – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?

Answer 1

Let a be subtracted from 2x² – 5x,
Dividing 2x² – 5x by 2x + 1,

`2x+1")"overline(2x^2-5x-a)"(x - 3`

            2x²+x               
            –      –
                  –6x – a
                  –6x – 3
                 +     +        
                  –a + 3       
Here remainder is (3 – a)
but we are given that remainder is 2.
∴ 3 – a = 2
⇒ –a = 2 – 3 = –1
⇒ a = 1
Hence 1 is to be subtracted.