2. 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.

Question

2.	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.

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

@ParthKohli  pleaase help me

anonymous · Answer

@shrutipande9

shrutipande9 · Answer

@ganeshie8

anonymous · Answer

he's not replying to me @shrutipande9

ganeshie8 · Answer

basically you need to find out who is correct based on `remainder` and `factor` theorems. familiar with them ?

anonymous · Answer

no :/

anonymous · Answer

oh wait is that when you find a factor and the remainder has to be 0? @ganeshie8

ganeshie8 · Answer

Yes :)  remainder theorem says this : 

`remainder of f(x)/(x-k) equals  f(k)`

ganeshie8 · Answer

here is factor theorem :

`if f(k) = 0, then (x-k) is a factor of f(x)`

ganeshie8 · Answer

use them to find out the correctness of given statemetns

ganeshie8 · Answer

`Professor McCoy: She says that 2 is a zero of g(x) because long division with (x + 2) results in a remainder of 0.`

which theorem applies here ?

anonymous · Answer

so which one should i use first?

anonymous · Answer

remainder theorem

ganeshie8 · Answer

Yes! She says dividing g(x) by (x+2) results in a remainder of 0 and so she concludes 2 is a zero. This is wrong because (x+2) = (x-(-2)). so -2 is the zero of g(x), NOT +2.

ganeshie8 · Answer

see if you can interpret remaining two ppl's statements similarly

anonymous · Answer

i need help with this •	Ms. Guerra: She says that 2 is a zero of g(x) because g(2) = 0.

ganeshie8 · Answer

thats actually the definition of zero of a function itself. we say "k" is a zero of f(x) if f(k) = 0. so...

anonymous · Answer

so g(2) will equal 0 as well?

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

the question is about deciding whether her reasoning is correct or not

anonymous · Answer

which is what i'm in need of help with

ganeshie8 · Answer

(continued)... she is right because she is correctly using the definition of zero of a function

ganeshie8 · Answer

watch this to make more sense of these two thms https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial-remainder-theorem-tutorial/v/polynomial-remainder-theorem-example

anonymous · Answer

okay i have one more please @ganeshie8

anonymous · Answer

okay i have one more please @ganeshie8