please help!! ill give a medal!!

Question

anonymous · Answer

Three party-goers 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 party-goers in full and complete sentences. Make sure you reference any theorems that support your justifications.

kc_kennylau · Answer

In order to know the answer quickly, you can use examples to help you understand. The simplest polynomial with 2 being a zero is definitely $x-2$.

anonymous · Answer

ok

kc_kennylau · Answer

Prof McCoy: $\dfrac{x-2}{x+2}$ definitely doesn't have a remainder of 0

kc_kennylau · Answer

Ms. Guerra: x-2=2-2=0

kc_kennylau · Answer

Mr. Romano:|dw:1387814070222:dw|