Question

Algebra 2 help please

Answer 1

List the polynomial’s zeroes with possible multiplicities.

Write a possible factored form of the seventh degree function.

Answer 2

@phi

Answer 3

the zeros are where the curve touches or crosses the x-axis

For multiplicities, see item #4 here
http://www.themathpage.com/aPreCalc/point-inflection.htm

Answer 4

So would I say "-5; even, -1; odd," etc. ?

Answer 5

-5 has an even multiplicity. (because it looks like a parabola that just touches the x-axis)

there is one other root that could be repeated. which one? hint: look at #4 part (b) in the above link.

Answer 6

Is it:
4 - odd.
7 - even

Answer 7

the zeros where the curve goes straight through the x-axis are *single roots*
that means 1 and 7.
that leaves -5 and 4 as the repeated roots.
you have a 7-degree polynomial... that means 7 roots. 2 we know are single roots (at 1 and 7).
that leaves 5 roots to find. where are they ?

Answer 8

Are all the roots on the X-axis? The line doesn't cross anywhere else, I'm confused..

Answer 9

yes, "roots" are where the y-value is 0. y=0 means you are on the x-axis.

Answer 10

Are the roots: -5,-3,-1,0,3,4,7

Answer 11

the roots are the x-values where the curve touches or crosses the x-axis.
-5 yes
-3 no

Answer 12

I thought I said them all earlier but you said there were more.

-5,-1,4,7,

Answer 13

There are 7 roots (a 7-degree polynomial has 7 roots... this is the fundamental theorem of algebra)
See http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

Answer 14

We see only 4, so some of those roots are repeated.

Answer 15

ohh

Answer 16

-1,4,7 ?

Answer 17

to find the repeated roots, we know that "repeated roots" have a special shape.
The roots that are not repeated (in other words they are just 1 root) are where the curve goes straight through the x-axis.

Two of the roots are just single roots. Can you list them?

Answer 18

-5 and 4

Answer 19

But isn't that only 6?

Answer 20

The roots that are not repeated (in other words they are just 1 root) are where the curve goes straight through the x-axis.

Two of the roots are just single roots. Can you list them?

Answer 21

-1 and 7

Answer 22

My bad

Answer 23

I have my answer for the first part as:

List the polynomial’s zeroes with possible multiplicities.

-5, -1, 4, 7

-1 and 7 = Single routes

-5 and 4 = Double roots

Is that correct?

Answer 24

That would only be 6 routes instead of 7, though.

Answer 25

almost. you need 7 roots all together.

Did you look at
http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html
?

one of the repeated roots is an *even* number 2 or 4
the other is an odd number 3,5 etc

Answer 26

I did but I thought it was -5 and 4, it doesn't go through the X axis at those points

Answer 27

you got that part correct. but repeated roots could be more than 2
in fact, if you have 2 roots at the same spot it has a certain shape.
look at #4 (a). Do you see what shape the curve is for 2 (or 4) roots at the same spot?

Answer 28

Parabola?

Answer 29

to be more clear: you have 7 roots. two of them are single roots at -1 and 7
that leaves 5 unaccounted for.
one of the remaining roots (at x= -5) is a repeated (an even number of times) root.
in other words it is a double root

the other root is a repeated (an odd # of times) root. See #4 (b) for its shape. In other words the root at 4 has an odd # of repeats. 1 does not count as a repeat, so that means 3,5,7 repeated roots.

we need 5 roots (besides the 2 we know are single roots). That means we have a 3 roots at 4, which leaves 2 roots (a double root) at -5.

Answer 30

So is this good as an answer?

-5, -1, 4, 7

-1 and 7 = Single roots

-5 = Double root

4 = Triple root

Answer 31

Yes. Here is a graph I made using those as the roots

Answer 32

Why is that graph different than the other?

Answer 33

They look pretty close to me. There is still an unknown factor out front, which I picked to be -18/100000 to make them look close.

Unless you are looking at a different graph ?

Answer 34

Oh, nevermind. They are very similar. Sorry I was thinking about a different graph

Answer 35

They seem to be exact

Answer 36

For the second part, what is a possible factored form of the seventh degree function?

Answer 37

what does "factored form" mean ?

Answer 38

I think the factored form would be like "x^3 + 3x^2 – 9x – 27"

Answer 39

Just an example ^

Answer 40

that is standard form

what do you do if they ask
factor x^2 +4x + 4
?

Answer 41

Simplify/combine like terms?

Answer 42

i gtg im sorry. thanks for all of ur help! ur amazing

Answer 43

factored means break into factors: (x+2)(x+2) is the factored form of
x^2 + 4x + 4

Answer 44

Hey @phi I'm back if you don't mind helping me finish this.

Answer 45

@phi