Question

ILL FAN MEDAL ANYTHING
A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones.

Their suggestions are:

(x – 1)
(x + 2)
(x – 3)
(x + 4)
(x + 6)
(x – 12)
List the correct factors. Then justify your selections with complete sentences.

Answer 1

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. Make sure you reference any theorems that support your justifications.

Dr. Collier summons you over to his table. He wants to demonstrate the graph of a fourth-degree polynomial function, but the batteries in his graphing calculator have run out of juice. Explain to Dr. Collier how to create a rough sketch of a graph of a fourth-degree polynomial function.
Mrs. Collins is at the table with you and states that the fourth-degree graphs she has seen have 4 real zeros. She asks you if it is possible to create a fourth-degree polynomial with only 2 real zeros. Demonstrate how to do this and explain your steps.

Answer 2

@misty1212

Answer 3

@misty1212

Answer 4

HI!!

Answer 5

what a long winded question! guess we have to cut through all the verbiage to see what it is really asking

Answer 6

Professor McCoy: She says that 2 is a zero of g(x) because long division with (x + 2) results in a remainder of 0.
that is INCORRECT
if \(g(2)=0\) then long division by \(x-2\) would leave a remainder of 0, not \(x+2\)

Answer 7

SO HE IS WRONG ?

Answer 8

yes that is INCORRECT

Answer 9

Ms. Guerra: She says that 2 is a zero of g(x) because g(2) = 0.
that is CORRECT because that is what it means to say \(2\) is a zero
it means \(g(2)=0\)

Answer 10

Mr. Romano: He says that 2 is a zero of g(x) because synthetic division with 2 results in a remainder of 0.
that is also CORRECT
the remainder is the same as \(g(2)\) so if the remainder is 0, that means \(g(2)=0\)

Answer 11

ok so i dont get what i do for any of the questions

Answer 12

which ones? i just answered 1 to 3

Answer 13

huh ?

Answer 14

where

Answer 15

i mean they are answered above

Answer 16

were

Answer 17

what are answred ? @satellite73

Answer 18

i need questions 2 and 4 !!! plz

Answer 19

@misty1212