Adding Polynomials – Practice Problems

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To work with polynomials, it’s important to know the lexicon, the language associated with polynomials: term, constant, monomial, binomial, trinomial, degree, like terms, and unlike terms. Polynomials are made up of terms. Terms can be variables alone, variables with exponents, and variables with coefficients with or without exponents. Terms can also be numbers which are called constants. Constants are really just numbers multiplied by xº (which is equal to one), but the variable and exponent are hidden - be aware that it exists.

A polynomial with one term is called a monomial; two terms is a binomial; three terms is a trinomial. More than that, we just call it a polynomial, so a polynomial with fifty terms is called a polynomial. How can you stay organized to do operations with polynomials? Before you can do an operation such as adding, put the terms in the standard form which is ordered by the degree of each term, from highest to lowest. The degree is determined by the exponent and for two or more variables in a term, the sum of the exponents.

Once polynomials are ordered in standard form, you can add the like terms. Like terms have the same variable and the same degree. Sometimes an unlike term can look the same as a like term, so be careful. To help you learn the language of polynomials and how to add the like terms of polynomials, press play so you can watch this video.

Perform arithmetic operations on polynomials.


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Exercises in this Practice Problem
Find out how much space the tents and the stage take up by adding the polynomials.
Add the polynomials vertically to find the combined space needed for tents and for the stage.
Identify the degrees of the given monomials.
Calculate the total space needed for the birthday party by adding the two polynomials.
Determine the degrees of the monomials.
Simplify the given polynomials by combining all like monomials.