Question

Can someone please help me fill in the blanks?
m(x)=x+x^2-1
Standard polynomial form: x^2+x-1
Polynomial name: ?
Degree: I think the degree is 3?
Leading coefficient?
Constant term: -1

Answer 1

here are the names of polynomials: [i'd write these down somewhere so you can have them for later]

name | equation form | Degree
constant c 0
linear x + c 1
quadratic x^2 +x + c 2
cubic x^3+x^2 +x + c 3
quartic x^4+x^3+x^2 +x + c 4

Answer 2

as for "leading coefficient"
it means the coefficient of the term that has the biggest power

Answer 3

so the name of this polynomial would be quadratic? I am confused on the degree part though, I thought you added the exponents to find the degree of the polynomial, is that wrong?

Answer 4

So the leading coefficient would just be: x^2 ?

Answer 5

i'll double check on the degree, but i'm pretty sure 'degree' is just another way to say the polynomial name...

the leading term is x^2 but the coefficient needs to be a number, does that help?

Answer 6

Here is the question if this helps!

Answer 7

That does help, but since the leading coefficient is x^2 and there is no number, what exactly would I put down as the leading coefficient then?

Answer 8

I looked on wolfram alpha and basic mathmatics web pages and they both say it's the way I posted

Answer 9

Okay, I trust you! :) so then this one would be a Quadratic polynomial?

Answer 10

here is a link for degree, if you wanna check it out yourself ^_^
http://www.basic-mathematics.com/degree-of-a-polynomial.html

Answer 11

yep, quadratic polynomial

Answer 12

with a leading coefficient of x^2? :)

Answer 13

oh wait

Answer 14

"with a leading coefficient of x^2?"
so the 'leading term' would be "x^2"
but the leading coefficient is a number infront of the term with the largest power
remember that x^2 is really 1x^2?
so the leading coefficient is 1

Answer 15

OH that makes sense!

Answer 16

^_^

Answer 17

thank you!! :) do you think you could help me out with 2 more problems similar to the one we just did to make sure I get them right? :)

Answer 18

ya, you can just post them up here if yo want

Answer 19

okay, thank you! :) so the next one is:
\[d(x)=x+\pi\]

Standard form:
Polynomial name:
Degree:
Leading Coefficient:
Constant term:

This one is really throwing me off because I have never worked with pi :o

Answer 20

pi can be weird at first, but believe it or not pi is a 'constant' meaning treat the pi term just like you would if it were a 1 or a 2 or any number

Answer 21

so in this case the constant would be 3.14?

Answer 22

the constant would be "π"
if you were asked to give it a number, then you could do 3.14, but I'd just write in "pi" or "π" as my answer ^_^
good questions!

Answer 23

awesome, thanks! :) so how would I fill in the rest though? like what would the standard form be, what would the name of this polynomial be, would the degree be 1, and would the leading coefficient be 1?

Answer 24

you got this and this right:
"would the degree be 1, and would the leading coefficient be 1?"
I bet you can get the rest,

you know the degree is 1, use the table I gave you and tell me what you think ^_^

Answer 25

that's right! for the polynomial name, I got linear, so would the standard form be the same as it is written? d(x)=x+π

Answer 26

exactly! nice work ^_^

Answer 27

you're getting the hang of it

Answer 28

okay, one more! :)

Answer 29

ya!

Answer 30

\[w(x)=2-6x^2+11x^3\]

Standard form: 11x^3-6x^2+2
Polynomial name: Quadratic
Degree: 2
Leading Coefficient: 11
Constant term: 2

Is that right?

Answer 31

Standard form: 11x^3-6x^2+2 [correct]
Polynomial name: Quadratic [use the table above, there is a "x^3" term in this]
Degree: 2 [degree would be 2 If your largest power was "x^2"]
Leading Coefficient: 11 [correct]
Constant term: 2 [correct]

Answer 32

oh okay! so it is cubic with a degree of 3?

Answer 33

yep! ^_^

Answer 34

wow thank you so much youre awesome!!!! :)

Answer 35

^_^
thx

Answer 36

no thank you! :)

Answer 37

hey, I was thinking a few days later now, that I may have misunderstood the question you posted.
I messed up in the difference is the naming of degrees and polynomials. I told you wrong the first time, I said the name of the degree was the polynomial name. so here is the correct way.

polynomial name | examples
monomial x, a^2b^3, x^4 <- one term in equation
binomial x^2+3, ab+x <-two terms
trinomial x^2+x+3, ab+b+2 <-three terms



and here is what I should have said before:

degree | degree name
1 linear
2 quadratic
3 cubic