Question

Part 1: Determine whether 2 is a zero of the polynomial P(x) = 3x3 – 6x2 – 3x – 18 by using the Remainder Theorem. Show your work. (4 points)

Part 2: Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function. (4 points)

Answer 1

i believe the remainder thrm says; if P(2) = 0, its a zero

Answer 2

which to me seems rather redundant. How to determine of a given value is a zero? plug it in and see if you get a zero ...

Answer 3

i've been using purple math to help me, but i just got stuck on this problem. can you teach it to me step by step please?

Answer 4

i can, but what method are you wanting to use?

Answer 5

synthetic or long hand?

Answer 6

synthetic please

Answer 7

synthetic requires that all the positions be accounted for; in other words; the coeffs of the x^n parts in descending order all have to be there.

3x3 – 6x2 – 3x – 18
3 2 1 0

this HAS all its parts so no zeros need to fill in; so strip it down to coeffs

3 -6 -3 -18

we good so far?

Answer 8

yepp!

Answer 9

good

now we can proceed with the set up:

start with an initial 0 in the add row and set up your "zero" in the multiply row


3 -6 -3 -18
0 <------ add this row
----------------
2) <----- multiply this row


this make sense?

Answer 10

yepp, good so far (:

Answer 11

i set it up this way as opposed to the confusing and self defeating format

Answer 12

lets start by adding our 3+0

take that result and multiply it by our 2, and stick that result into the add row


3 -6 -3 -18
0 3(2) <------ add this row
----------------
2) 3 <----- multiply this row

this process is repeated to the end

Answer 13

3 -6 -3 -18
0 6 0 -6
----------------
2) 3 0 -3 -24 <-- this last number is the value we get for P(2)

Answer 14

if that last value is a 0, then P(2) = 0 and 2 would have been a root

Answer 15

ohhhh i get it!!

Answer 16

thanks so much (:

Answer 17

good luck :)