monomial

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.

• Polynomial Regression

  • It is often difficult to interpret the individual coefficients in a polynomial regression fit, since the underlying monomials can be highly correlated.

• Rational Algebraic Expressions

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