Question

Use synthetic division and the Remainder theorem to find the function value: f(x)= 6x^3-27x^2-15x find f(-1/2).

Answer 1

I know how to do synthetic division but what is the remainder theorem?

Answer 2

I was confused about that part, and I can't find a clear answer.

Answer 3

well the remainder theorem basically requires you to substitute x = -1/2 into the equation and get a value....

if the value is 0 then x = -1/2 is a zero of the function

any other number, that's the remainder...

so I'd say you need to do the division... get the remainder

and then prove its the correct remainder by finding f(-1/2)

hope it makes sense.

Answer 4

Hmm, okay, that makes sense thank you. I had that as a question on a previous exam and none of the answers fit the way I was doing it before. So putting f(-1/2) is just to prove the remainder you got from synthetic division is correct?

Answer 5

that's it.... the substitution process is called the remainder theorem.

Answer 6

Thank you! :))