Table of Contents
All Types of Polynomials
A polynomial is an expression consisting of variables and coefficients, that is, numbers that are multiplied together. The coefficients are the numbers that appear in front of the variables.
A polynomial in a single variable, x, is written
axn
where a is the coefficient of xn and n is the degree of the polynomial. The degree is the largest exponent in the polynomial.
A polynomial in more than one variable is written
axnbym
where a, b, and m are the coefficients of xn, ym, and z0, respectively. The degree of a polynomial in more than one variable is the sum of the degrees of the individual polynomials that make it up.
A polynomial is always written with the variable(s) in parentheses and the coefficients outside the parentheses.
Some examples of polynomials are
2×3 + 5×2 − 3x
(x − 1)2
3x4y5 + 2x3y4
The first polynomial is a second-degree polynomial in one variable, x. The second polynomial is a first-degree polynomial in one variable, x. The third polynomial is a fourth-degree polynomial in two variables, x and y.
Polynomial Equation
A polynomial equation is an equation that contains a variable raised to a power greater than one. The variable can be a real number, or a complex number. The equation will always have at least one term, and may have multiple terms. The highest power of the variable is the degree of the polynomial equation.
What is Unique About Polynomials?
A polynomial is a mathematical expression that is composed of one or more terms, each of which is a product of a variable and a nonzero number. The variable appears in each term, and the powers of the variable are called the coefficients of the term. The polynomial’s highest power is called its degree. Polynomials are used in a variety of mathematical applications, including algebra, calculus, and physics.
One of the unique properties of polynomials is that they can be factored into a product of simpler polynomials. This factoring process can often be used to solve problems or find solutions to equations. Additionally, polynomials can be rearranged to form more convenient algebraic expressions.
Types of Polynomials
A polynomial is an expression that is the sum of a finite number of terms, each of which is a monomial.
A monomial is a product of a number, a variable, and a constant.
The degree of a polynomial is the largest degree of any one of its terms.
A polynomial has degree 0 if it is a constant.
A polynomial has degree 1 if it is a monomial.
A polynomial has degree 2 if it is the sum of two monomials.
A polynomial has degree 3 if it is the sum of three monomials.
A polynomial has degree 4 if it is the sum of four monomials.
A polynomial has degree 5 if it is the sum of five monomials.
A polynomial has degree 6 if it is the sum of six monomials.
A polynomial has degree 7 if it is the sum of seven monomials.
A polynomial has degree 8 if it is the sum of eight monomials.
A polynomial has degree 9 if it is the sum of nine monomials.
A polynomial has degree 10 if it is the sum of ten monomials.
Degree of a Polynomial Definition
A degree of a polynomial is the highest power of the variable in the polynomial.
