Question

One root of f (x) = x cubed + 10 x squared minus 25 x minus 250 is x = –10. What are all the roots of the function? Use the Remainder Theorem.

Answer 1

Hi and welcome to QuestionCove!
I used this video to help understand the Remainder Theorem more clearly: https://www.youtube.com/watch?v=bvxbC3W9trw&t=1s

We are given one root of the polynomial as x=-10, which means that one factor of the polynomial should be (x+10); indeed, if we take f(-10) of the equation, we do get a remainder of 0, which confirms that (x+10) is a factor of the function.

Perhaps you can divide the polynomial by (x+10) to get a smaller polynomial and then find the roots of that polynomial using the remainder function?