monomial

(noun)

An algebraic expression consisting of one term.

Related Terms

  • Monomials
  • Binomials
  • Multiplication of Two Monomials
  • Binomial
  • binomial
  • polynomial
  • commutative
  • trinomial

(noun)

A single term consisting of a product of numbers and variables.

Related Terms

  • Monomials
  • Binomials
  • Multiplication of Two Monomials
  • Binomial
  • binomial
  • polynomial
  • commutative
  • trinomial

(adjective)

Relative to an algebraic expression consisting of one term.

Related Terms

  • Monomials
  • Binomials
  • Multiplication of Two Monomials
  • Binomial
  • binomial
  • polynomial
  • commutative
  • trinomial

Examples of monomial in the following topics:

  • Multiplying Algebraic Expressions

    • The process for multiplying algebraic expressions differs for monomials and polynomials.
    • A monomial is a single term consisting of a product of numbers and variables.
    • The following are examples of monomials:
    • (Note that multiplying monomials is not the same as adding algebraic expressions—monomials do not have to involve "like terms" in order to be combined together through multiplication.)
    • The monomial should be multiplied by each term in the polynomial separately.
  • What Are Polynomials?

    • $7x^{\sqrt{2}}$, $\sqrt{2}x^{-7}$ and $2x^7 - 7x^2$are not monomials.
    • A polynomial over $\mathbb{R}$ is a finite sum of monomials over $\mathbb{R}$.
    • is the finite sum of the $4$ monomials: $4x^{13}, 3x^2, -\pi x$ and $1 = 1x^0.$
    • These monomials are called the terms of $P(x).
    • Every monomial is also a polynomial, as it can be written as a sum with one term, itself.
  • Multiplying Polynomials

    • Multiplying a polynomial by a monomial is a direct application of the distributive and associative properties.
    • So for the multiplication of a monomial with a polynomial we get the following procedure:
    • Multiply every term of the polynomial by the monomial and then add the resulting products together.
    • To multiply a polynomial $P(x) = M_1(x) + M_2(x) + \ldots + M_n(x)$ with a polynomial $Q(x) = N_1(x) + N_2(x) + \ldots + N_k(x)$, where both are written as a sum of monomials of distinct degrees, we get
  • Sums, Differences, Products, and Quotients

    • It is easiest to start with monomials.
    • A monomial equations has one term; a binomial has two terms; a trinomial has three terms.
  • Introduction to Factoring Polynomials

    • A polynomial consists of a sum of monomials.
  • Rational Algebraic Expressions

    • Rather, we will be looking for monomial and binomial factors that are common to both rational expressions.
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