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.

Question

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.

anonymous · Answer

Correct the reasoning of any inaccurate reasoning by the partygoers in full and complete sentences. Make sure you reference any theorems that support your justifications.

anonymous · Answer

The thing, is is that I dont see any problems with their reasoning. I mean, unless I have to say which theorem theyre referencing.

perl · Answer

professor Mccoy not necessarily correct.  if 2 is a 'zero' then long division with x-2 produces a remainder of zero

perl · Answer

if you do long division with x+2 and get a remainder of zero, then g(-2) = 0, not g(2) = 0