Question

Write a polynomial function of least degree with integral coefficients that has the given zeros. 3 multiplicity 2, -4

Answer 1

(x-2)^3(x+4)
multiply it and see if you can simplify afterward.

Answer 2

Foil right? (first outside inside last)

Answer 3

yeah basically. You can use the pascals triangle for the first part of the multiplicity (a-b)^3, then you multiply that by (x+4) and see if it simplifies

Answer 4

x3 +2x2 −15x+36 is this correct

Answer 5

x^3 + 2x^2 -15x +36

Answer 6

Actually I got
x^4-2x^3-12x^2+56x+32
Since
(x-2)^3 expands to x^3-6x^2+12x+8
and if you multiply that by (x+4) and combine like terms, you get
x^4-2x^3-12x^2+56x+32

Answer 7

oh ._. that isn't any of the multiple choice options

Answer 8

Wait, what is the highest degree polynomial that your multiple choices have?

Answer 9

the highest is a 3 degree monomial

Answer 10

http://www.wolframalpha.com/input/?i=%28x-2%29%28x-2%29%28x-2%29%28x%2B4%29
Can you see if any of the alternate forms listed here is one of your choices?

Answer 11

No I didn't see it but here are the choices

A) f(x)=x^3 −7x^2 −15x+36
B) f(x)=x^3 +2x^2 −15x+36
C) f(x)=x^3 −6x^2 −15x+36
D) f(x)=x^3 −2x^2 −15x+36

Answer 12

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\(\normalsize\color{red}\bigstar\large\color{gold}\bigstar\Large\color{greenyellow}\bigstar\large\color{cyan}\bigstar\normalsize\color{blue}\bigstar\large\color{purple}\bigstar\Large\color{magenta}\bigstar\large\color{pink}\bigstar\normalsize\color{orchid}\bigstar\large\color{red}\bigstar\Large\color{gold}\bigstar\large\color{greenyellow}\bigstar\Large\color{cyan}\bigstar\large\color{blue}\bigstar\normalsize\color{purple}\bigstar\large\color{magenta}\bigstar\Large\color{pink}\bigstar\large\color{orchid}\bigstar\normalsize\color{red}\bigstar\)

Answer 13

O.O thanks

Answer 14

Bahah you are welcome xd

Answer 15

xD*

Answer 16

A) f(x)=x^3 −7x^2 −15x+36
B) f(x)=x^3 +2x^2 −15x+36
C) f(x)=x^3 −6x^2 −15x+36
D) f(x)=x^3 −2x^2 −15x+36

just incase you missed them here are the choices :)

Answer 17

youre setup is a little flawed, good concept, but just written a little off

Answer 18

the roots are: 3,3,-4 , not 2,2,2,-4

Answer 19

Mine? I have no setup I'm trying to teach this to myself my math teacher doesn't make sense ._.
and thank you :D though I still have no clue what I'm doing

Answer 20

the first response had a good idea, but just read the information incorrectly

(x-3)(x-3)(x--4) is corrected as

(x-3)^2 (x+4)

Answer 21

the rest is just multiplicating it all out to polynomial form

Answer 22

multiplying (x-3)(x-3) gets us

x-3
x-3
----
x^2 -3x
-3x +9
-----------
x^2 -6x + 9

multiplying that by x+4 we get

x^2 -6x + 9
x +4
------------
x^3 -6x^2 + 9x
4x^2 -24x +36
---------------------
add em up

Answer 23

and feel free to ask any questions about what just happened

Answer 24

X^3 + 4x^2-30x+40?
I'm gonna fail

Answer 25

your adding skills need work

Answer 26

x^3 -6x^2 + 9x
4x^2 -24x +36
---------------------
x^3 -2x^2 -15x +36

Answer 27

oh ._.

Answer 28

x-3
x-3
----
x^2 -3x
-3x +9
-----------
x^2 -6x + 9

multiplying that by x+4 we get

x^2 -6x + 9
x +4
------------
x^3 -6x^2 + 9x
4x^2 -24x +36
---------------------
add em up


Can you explain this to me because I have 3 more questions like this and i'm about to pull my hair out :c

Answer 29

ok, multiplication hasnt changed since like the 3rd grade; so all we are doing is multiplying stuff in teh same fashion

Answer 30

There wasn't really a reason for you to be rude but thanks anyway

Answer 31

x-3
x-3
----

it doesnt matter which term we start with, i just like to start from left to right, right to left is the usual number way to do it tho soo for comparison

x-3
x-3
------
-3x+9

Answer 32

sigh .. im not being rude

Answer 33

being rude is like this: "if you are soo stupid that .... blah blah blah"

i am not being rude by stating that multiplication hasnt changed and that if you recall how to multiply numbers, then this is just as simple to do

Answer 34

now, to continue on the demonstration ....

now we can multiply the x term in the same fashion, drop down and stagger the row

x-3
x-3
----------
-3x+9
x^2 -3x

now, like usual, we add up the rows

Answer 35

its the exact same process, nothing has changed.

Answer 36

i format it from left to right, it just lines up simpler while typing on here

x-3
x-3
------
x^2 -3x
-3x +9
-----------
x^2 -6x + 9

does that make sense?

Answer 37

I just want to know where the x+4 comes from

Answer 38

we have three roots to deal with: 3,3,-4

each root makes the equation equal to 0

x-3, x-3, and x+4 form the factors for the equation. as such

f(x) = (x-3)(x-3)(x+4)

when x=3, we get a zero, and when x=-4 we get a zero ... agreed?

Answer 39

yup

Answer 40

then we need to expand this out ... multiply the parts together to put it into the format that the options give.

Answer 41

that isn't going to work for my new equation there is only one zero. -1 with a multiplicity of 3

Answer 42

you have to form the factors from the stated roots: -1,-1,-1

do you agree that: (x+1)(x+1)(x+1) fits the information?

Answer 43

yup

Answer 44

then its just a matter of multilying it out in whatever fashion suits you best

Answer 45

So is the answer x^3 +3x +1

Answer 46

x+1
x+1
------
x^2 +x
x + 1
-----------
x^2 +2x + 1




x^2 +2x + 1
x + 1
-------------
x^3 +2x^2 +x
x^2 +2x + 1
-------------------
x^3 +3x^2 +3x +1

Answer 47

why is it only x+1 x+1 should't there be three because there is a multiplicity of 3

Answer 48

ive never learned to multiply 3 numbers together at the same time

Answer 49

so i tend to work it in pairs

Answer 50

k

Answer 51

(x+1)(x+1) = x^2 +2x + 1

(x^2 +2x + 1)(x+1) = x^3 + 3x^2 + 3x + 1

therefore

(x+1)(x+1)(x+1) = x^3 + 3x^2 + 3x + 1