Asked by: Kirsti Pruene
technology and computing information and network security

What are polynomial expressions and how do you simplify them?

Last Updated: 17th June, 2020

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Identify like terms in a long polynomial and combine them to get a simplified polynomial. Like terms have the exact same variables and exponents; only the coefficients are different. To simplify like terms just add or subtract the coefficients.

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Besides, what are polynomial expressions?

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.

Also, what are coefficients? In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. For example, if y is considered as a parameter in the above expression, the coefficient of x is −3y, and the constant coefficient is 1.5 + y.

Beside this, how do you simplify expressions?

Here are the basic steps to follow to simplify an algebraic expression:

  1. remove parentheses by multiplying factors.
  2. use exponent rules to remove parentheses in terms with exponents.
  3. combine like terms by adding coefficients.
  4. combine the constants.

What is polynomial formula?

Polynomial Equations Formula Usually, the polynomial equation is expressed in the form of an(xn). Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.

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What is a zero polynomial?

Zero Polynomial. The constant polynomial. whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. The zero polynomial is the additive identity of the additive group of polynomials.

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What are the types of polynomials?

Types of Polynomials are Monomial, Binomial, Trinomial. Monomial is the polynomial with one term, Binomial is the polynomial with two unlike terms, and Trinomial is the polynomial with three, unlike terms.

Patrycia Remus

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Who invented polynomials?

Rene Descartes

Thi Ordonez

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Is Pi a polynomial?

Pi (π) is not considered as a polynomial. It is a value referring to the circumference of a circle. On the other hand, polynomial refers to an equation containing four variables or more.

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Is 8x a polynomial?

The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s). Examples: 3x4+4x2The highest exponent is the 4 so this is a 4th degree binomial. 8x-1 While it appears there is no exponent, the x has an understood exponent of 1; therefore, this is a 1st degree binomial.

Yousra Bim-Bad

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What is a rational expression?

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions.

Mykola Nesselrode

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How do you solve exponents?

To solve basic exponents, multiply the base number repeatedly for the number of factors represented by the exponent. If you need to add or subtract exponents, the numbers must have the same base and exponent.

Gaumet Holtgreife

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How do you simplify powers?

To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = 215. For any positive number x and integers a and b: (xa)b= xa· b. Simplify.

Cesarea Weiler

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How do you know the order of a polynomial?

Order of a polynomial
  1. the degree of a polynomial, that is, the largest exponent (for a univariate polynomial) or the largest sum of exponents (for a multivariate polynomial) in any of its monomials;
  2. the multiplicative order, that is, the number of times the polynomial is divisible by some value;