Question

Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.

Answer 1

f(x)=ax^3+bx^2+cx+d
f(-2)=-4
f(-2)=-8a+4b-2c+d=-4
just find some coefficient that give -4 as the result for the above
let a=1
b=1
c=2
d=1
so we have f(x)=x^3+x^2+2x+1

Answer 2

wait it didn't work
i made a mistake somewhere

Answer 3

oh i see my mistake lol
-8(1)+4(1)-2(2)+1 does not give -4 lol

Answer 4

-8(1)+4(1)-2(2)+4=-4
right?
so a=1
b=1
c=2
d=4

Answer 5

f(x)=x^3+x^2+2x+4

Answer 6

that works

Answer 7

you could chose anynumbers satisfying -8a+4b-2c+d=-4
as long as a is not zero since it wants a polynomial of degree 3

Answer 8

true

Answer 9

a=1
b=1
c=0
d=0
f(x)=x^3+x^2 is another one

Answer 10

do you know the quotient

Answer 11

i mean f(x)=x^3+x^2+2x+4

Answer 12

x^2-x+4

Answer 13

okay okay hold sooo first i have too set up the synthetic division problem which is ??? :) im trying too do it step by step first

Answer 14

what polynomial do you want to use?

Answer 15

i can use the one you gave me but it has too be something like for example x^2-2x+4 by x-6

Answer 16

myininaya sorry to bother you but can you have a look at my question when your done:)

http://openstudy.com/groups/mathematics/updates/4dff1c2a0b8bbe4f12e764cb

Answer 17

so you want to divide x^2-2x+4 by x-6?
why are we doing this?

Answer 18

okay and

Answer 19

is this a separate problem?

Answer 20

boo?

Answer 21

6| 1 -2 4
| 6 24
________________
1 4 | 28
so x^2-2x+4 divided by x-6= x+4 +28/(x-6)

Answer 22

this doesn't have anything to do with the initial problem you asked except x^2-2x+4 is the quotient if we chose f(x)=x^3+x^2+2x+4 where remainder is -4

Answer 23

okay so we can choose the f(x)=x^3+x^2+2x+4 where the remainder is 4 but the same way the other example was solved thats how my teacher wants meh too solve this question that i am asking

Answer 24

remainder is -4
and im sorry what is the question you are asking exactly?

Answer 25

Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.

Answer 26

we already this though

Answer 27

a polynomial of degree 3 is f(x)=ax^3+bx^2+cx+d
we are also given that it should satisy f(-2)=-4
f(-2)=a(-2)^3+b(-2)^2+c(-2)+d=-8a+4b-2c+d=-4
-8a+4b-2c+d=-4
you can choose and polynomial in the form ax^3+bx^2+cx+d such that when you do
-8a+4b-2c+d you must get -4
you can choose any values for a, b, c, and d as long as it satisfies -8a+4b-2c+d=-4
and d does not equal zero since we want a poly of degree 3

Answer 28

okay i get ittttttt