Question

x^3-ax^+6-a is divided by x-a​

Answer 1

Let p(x) be any polynomial of degree greater than or equal to one and let 'a' be any real number. If a polynomial p(x) is divided by x - a then the remainder is p(a).

Let p(x) = x3 - ax2 + 6x - a

The root of x - a = 0 is a.

p(a) = (a)3 - a(a)2 + 6(a) - a

= a3 - a3 + 5a

= 5a

Hence by remainder theorem, 5a is the remainder when x3 - ax2 + 6x - a is divided by x - a.