Question

Three partygoers are in the corner of the ballroom having an intense argument. You walk over to settle the debate. They are discussing a function g(x). You take out your notepad and jot down their statements.
Professor McCoy: She says that 2 is a zero of g(x) because long division with (x + 2) results in a remainder of 0.
Ms. Guerra: She says that 2 is a zero of g(x) because g(2) = 0.
Mr. Romano: He says that 2 is a zero of g(x) because synthetic division with 2 results in a remainder of 0.
Correct the reasoning of any inaccurate reasoning by the partygoers in full and complete sentences.

Answer 1

Please help I dont get this. I will reward a medal and fan you!

Answer 2

@leon549

Answer 3

@dahlindubs11

Answer 4

@israa88

Answer 5

first one is right

Answer 6

Can you tell me why?

Answer 7

No, I think the last two are correct. Do you know why?

Answer 8

because he made that choice after solving the hole problem

Answer 9

Prof. McCoy should have said (x-2) not (x+2).

Answer 10

second one is wrong because he just put the value of x in the eq without solving the eq

Answer 11

The factor theorem says that:
If f(a)=0, then (x-a) is a factor


The remainder theorem says that:
If (x-a) is a factor of f(x), then f(x)x−a=0

Answer 12

yeah i din't see that

Answer 13

So @LexiLuvv2431 : Did you understand anthing I said?

Answer 14

@LexiLuvv2431:
So say that 2 is indeed a zero of f(x), then a factor must be (x-2) according to the first which then supports Ms. Guerra and also if (x-2) really is a factor as Ms. Guerra says then we can understand that f(x)x−2=0 which supports Mr. Romano conjecture.

Answer 15

Does this help?

Answer 16

Yess I kinda get it. So is Ms. Guerra right?

Answer 17

Yes. And so is Mr.Romano.

Answer 18

Ohh okayy I see. Thank you!

Answer 19

Anytime. :)