Question

If two polynomials (ax^3+4x^2+3x-4) and (x^3-4x+a) leaves the same remainder when divided by (x-3) find the value of a

Answer 1

Answer:

as the remainders are equal, both can be equalized.

$a {x}^{3} + 4 {x}^{2} + 3x - 4 = {x}^{3} - 4x + a$

and given that, x-3=0

×=3

substituting this in the equation,

$a( {3})^{3} + 4 ({3})^{2} + 3(3) - 4 = ({3})^{3} - 4(3) + a \\ 27a + 36 + 9 - 4 = 27 - 12 + a \\ = 27a - a = 15 - 41 \\ 26a = - 26 \\ a = - 1$