Question

The polynomial f(x) = `x^3 + 3x^2 + ax + b` leaves the same remainder when divided by `(x – 2)` as when divided by `(x +1)`. Find the value of `a`?

Answer 1

`a=-6`

Explanation:

`f(x)=x^3+3x^2+ax+b`
`f(2)=2^3+3*2^2+2a+b=R_1`
`R_1=2a+b+20`
`f(-1)= (-1)^3+3*(-1)^2-a+b=R_2`
`R_2=-a+b+2`
`R_1=R_2`
`2a+b+20=-a+b+2`
`3a=-18`
`a=-6`