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By — McGraw-Hill Professional
Updated on Sep 26, 2011

Monomials and Polynomials

An algebraic expression consists of variables (letters), constants (numbers), operation signs, and grouping symbols. Also recall that a term of an algebraic expression consists of a number, variable, or a product or quotient of numbers and variables. The terms of an algebraic expression are connected by + or - signs. An algebraic expression consisting only of the four operations (addition, subtraction, multiplication, and division), and which has no variable in the denominator of a term, is called a polynomial . If the expression has one term, it is called a monomial . If the expression has two terms, it is called a binomial . If the expression has three terms, it is called a trinomial .

Recall that only like terms can be added or subtracted. For example, 5x + 6x = 11x. Unlike terms cannot be added or subtracted.

Example 1

Add (3x 2 + 2x –5) + (5x 2 – 7x + 3)

Solution 1

Math Note: Recall that when the numerical coefficient is one, it is not written: i.e., xy = 1xy. Likewise -xy = -1xy.

Example 2

Add (2x + y) + (2x – 5) + (3y – 7).

Solution 2

Math Note: If the sum of two like terms is 0, do not write the term in the sum.

Practice

1. (6x 2 + 3x – 8) + (2x 2 – 5x – 9)

2. (3x + 2y – 2) + (4x – 2y + 8)

3. (2x + 5) + (7x – 10) + (3x – 4) + (4x – 6)

4. (3a 2 b 2 + 5) + (a 2 b 2 + 2ab +4)

5. (9m + 5n – 2) + (4n – 8) + (6m + 7)

1. 8x 2 – 2x – 17

2. 7x + 6

3. 16x – 15

4. 4a 2 b 2 + 9

5. 15m + 9n – 3

Practice problems for these concepts can be found at: Operations with Monomials and Polynomials Practice Test.

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