Question

What is the remainder when `p(x) = x ^99 +2x^89+ 3x^79+4x^69+ 5x^59 +6x^49+7x^39 +8x^29+9x^19 +10x^9+11`is divided by`x-1`?

Answer 1

There is a remainder of `66`.

Explanation:

Use the remainder theorem, which states that if `x - a` is a factor of `p(x)`, then `p(a)` gives the remainder.

`p(1) = 1+ 2 + 3 + 4 + 5+ 6 + 7 + 8 + 9+ 10 + 11 = 66`

So the remainder is of `66`.

Hopefully this helps!