Question

Create your own polynomial with a degree of 3 that when divided by x + 2 has a remainder of -4

Answer 1

what do you have so far?

Answer 2

Nothing, this is to help someone out and this is all she wrote me. I don't know anything about this yet.

Answer 3

Well I will tell you some things to start you off
Say we called the polynomial f(x)
We are given f(-2)=-4

Answer 4

You need at least two terms.

Answer 5

actually you only need one term

Answer 6

or at least one term anyways

Answer 7

but whatever the polynomial is you must have x^3 somewhere up in there

Answer 8

f(x)=ax^3 <-- so you can choose this

Answer 9

f(x)=x^3+b <--this

Answer 10

and there are a lot more varieties you can choose

Answer 11

but you must apply the f(-2)=-4

Answer 12

How does f(-2)=-4 get brought into f(x)=ax^3?

Answer 13

f(-2)=-4
means replace x with -2
and when the x=-2 the expression =-4

Answer 14

so you can find what that little value a is

Answer 15

The expression being f(x)=ax^3?

Answer 16

the expression ax^3 was named f(x)

Answer 17

How would you find a?

Answer 18

by using f(-2)=-4

Answer 19

this was given in the problem

Answer 20

What do I do with f(-2)=-4, then?

Answer 21

you apply it to your function we called f

Answer 22

remember f(x)=ax^3

Answer 23

use f(-2)=-4 to find a

Answer 24

f(-2)=-4
says to replace x with -2
and at x=-2 your expression=-4

Answer 25

Your expression being f(x)=ax^3?

Answer 26

pretend like we have g(x)=9x+c
and I wanted to find c and I was given g(3)=4
g(3)=4 means we have g(3)=9(3)+c=4
so we have 9(3)+c=4
so 27+c=4
then c=4-27=-23
so g(x)=9x-23

Answer 27

g(3)=4 means when x=3 the expression we called g is 4
replace x with 3
the expression at x=3, is 4
so we have 9(3)+c=4
---

Answer 28

you need to apply f(-2)=-4 to f(x)=ax^3 to find a

Answer 29

So it'd be f(-2)=a(-2)^3=-4?

Answer 30

yep now solve for a

Answer 31

-8a=-4, divide the -8
a=0.5 ?

Answer 32

yep
you have found a function that works

Answer 33

f(x)=.5x^3 or x^3/2
since 1/2=.5

Answer 34

Yeah. How'd you get the 2nd function?

Answer 35

f(x)=ax^3 <- that one

Answer 36

f(x)=x^3+b <- or this one