Question

List all possible rational Zeros for the given function:
f(x)=x^3-8x^2-37x+44

Answer 1

This is a third degree polynomial, so there will be 3 zeros. You know that, right?

Answer 2

yes

Answer 3

How do u find the possible zero

Answer 4

Ok, so the trick here is to find what those zeros are. By ANY chance at all are you familiar with the rational roots theorem?

Answer 5

yes

Answer 6

Oh yay! Using the RRT, we know that the possible factors are those that go into the last constant and the first coefficient. The first coefficient is 1, so we really don't have to worry about including that in our list of possibles because it will show up when we list the factors of 44. The numbers that go into 44 are (and don't forget their negatives, as well)

Answer 7

\[\pm1, \pm2, \pm4, \pm11, \pm22, \pm44\]To make our lives simple, let's start with positive 1. Do you know synthetic division?

Answer 8

You must if you are studying the Rational Roots Theorem!

Answer 9

yes, we have to check sac one that can give us a remainder of zero

Answer 10

each*

Answer 11

Yep!! Great! Let's use synthetic division here with 1 to see if we get a 0 remainder.