MHB Can a polynomial ever just have 2 terms?

  • Thread starter Thread starter OMGMathPLS
  • Start date Start date
  • Tags Tags
    Polynomial Terms
Click For Summary
SUMMARY

A polynomial can consist of one or more terms, with specific classifications based on the number of terms: a monomial (one term), a binomial (two terms), and a trinomial (three terms). The discussion clarifies that a polynomial can indeed have two terms, as exemplified by expressions like x² - 4. Additionally, polynomials can include operations of addition, subtraction, multiplication, and non-negative integer exponents, but division is not permitted unless it can be expressed as multiplication by a constant. The classification of polynomials extends to their order, such as constant, linear, quadratic, cubic, and so forth.

PREREQUISITES
  • Understanding of polynomial definitions and classifications
  • Familiarity with mathematical operations: addition, subtraction, multiplication
  • Knowledge of polynomial order and terminology (e.g., monomial, binomial, trinomial)
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study polynomial classification in-depth, focusing on monomials, binomials, and trinomials
  • Learn about polynomial operations and their properties
  • Explore polynomial division and its implications in algebra
  • Investigate the significance of polynomial order and its applications in mathematics
USEFUL FOR

Students, educators, and anyone interested in understanding polynomial expressions and their classifications in mathematics.

OMGMathPLS
Messages
64
Reaction score
0
Or does it always have to have MORE THAN 2 like

x^2 +x^2 -4a polynomial can never be

x^2 - x-^3

Right?
 
Mathematics news on Phys.org
i don't fully understand your question but yes there can be x^2 and x^3 and x^4 and x^5 etc...
 
Whoops. Sorry I mean

A polynomial can never be

term +/-/*/divide term (only 2 terms)

it must be

term term term

at least 3 right? To be considered a polynomial?
 
In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

A polynomial can have as few as 1 term, which is a monomial. Two terms and the polynomial can also be called a binomial, and 3 terms is a trinomial. I tend to use the special names for smaller polynomials though. Also, polynomials in one variable have special names related to the order. Instead of using trinomial, I would call $x^2+x+1$ a quadratic, meaning it is a second order polynomial, because the largest exponent is 2.

With regard to order, there are constant, linear, quadratic, cubic, quartic, quintic, etc. polynomials.
 
well you can have something like $x^2-4$ which is only two terms and a polynomial CAN include division like $x^2/2...$
 
Oh ok. Thanks.

The Issac Newton picture fits you.
 
lol mark is isaac Newton.
 
ineedhelpnow said:
...a polynomial CAN include division like $x^2/2...$

Good point, but we could also view this as multiplication by 1/2. I think the restriction of not allowing division would be as in the following example:

$$\frac{x^2+x+1}{7x+2}$$

is not a polynomial, whereas,

$$\left(x^2+x+1\right)(7x+2)$$

is a polynomial, written in factored form.
 
OMGMathPLS said:
Oh ok. Thanks.

The Issac Newton picture fits you.

Hey, I never noticed that, but Geddy Lee does bear a certain resemblance to Newton. (Smirk)
 
  • #10
Lol
 
  • #11
OMGMathPLS said:
Lol

Just so you know for the future, we try to discourage the use of "textspeak" abbreviations, simply because we want to appeal to as wide a global audience as possible, and many folks around the world may not be familiar with these abbreviations and would be left wondering what it means. :D
 
  • #12
MarkFL said:
Hey, I never noticed that, but Geddy Lee does bear a certain resemblance to Newton. (Smirk)
Soooooo... Can we drop apples on him?

-Dan
 

Similar threads

High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
4K
High School Complete the square, yes, but what does it mean?
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad Proof for interpolating polynomial and error approximation
  • · Replies 6 ·
Replies
6
Views
2K
MHB Can you factor the following two polynomials?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Can the polynomial equation $x^8-x^7+x^2-x+15=0$ have real roots?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prove No Integers Solve $ax^3+bx^2+cx+d=1$ for x=19,2 for x=62
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Does Transforming Hermite Polynomials Affect Their Orthogonality?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prove Product of Polynomials: No Odd Degree Terms
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad What type is a polynomial function?
  • · Replies 7 ·
Replies
7
Views
2K