Question

What will the remainder be when P(x)=x^13+4x^7-3x+2?
How can I do this without dividing everything out?

Answer 1

You have not mentioned what P(x) is divided by.

Answer 2

ahh. sorry. when it is divided by x-1.

Answer 3

There is a remainder theorem that says if f(x) is divided by (x-a) then the remainder will be f(a).

So P(x) / (x-1) will have a remainder of P(1).

Answer 4

So P(1)=4?

Answer 5

Yes and 4 will be the remainder if you actually divide it out.

Answer 6

Right. Thank you!

Answer 7

You are welcome.