If the polynomials `a x^3+4x^2+3x-4` and `x^3-4x+a` leave the same remainder when divided by `(x-3),` find the value of `adot`

Explanation

Solution
Let `p(x) = ax³ + 4x² + 3x - 4` and `q(x) = x³ - 4x + a` be the given polynomials.
When `p(x)` and `q(x)` are divided by `(x - 3)` the remainder are `p(3)` and `q(3)` respectively.
`p(3) = q(3)` given
`a(3)³ + 4(3)² + 3 x 3 - 4 = 3^3 - 4*3 + a`
`27a +36 +9-4=27 - 12 + a`
`26a =15 - 41`
`⇒ 26a = -26 :.a =-26/26= -1.`