Classifying Polynomials

Polynomials can be classified two different ways - by the number of terms and by their degree.

1. Number of terms.

  • A monomial has just one term. For example, 4x2 .Remember that a term contains both the variable(s) and its coefficient (the number in front of it.) So the is just one term.

  • A binomial has two terms. For example: 5x2 -4x

  • A trinomial has three terms. For example: 3y2+5y-2

  • Any polynomial with four or more terms is just called a polynomial. For example: 2y5+ 7y3- 5y2+9y-2

Practice classifying these polynomials by the number of terms:

1. 5y

2. 3x2-3x+1

3. 5y-10

4. 8xy

5. 3x4+x2-5x+9

Answers: 1) Monomial 2) Trinomial 3) Binomial 4) Monomial 5) Polynomial

2. Degree. The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s).

  • 5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.

  • 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.

  • 5 There is no variable at all. Therefore, this is a 0 degree monomial. It is 0 degree because x0=1. So technically, 5 could be written as 5x0.

  • 3x2y5 Since both variables are part of the same term, we must add their exponents together to determine the degree. 2+5=7 so this is a 7th degree monomial.

Classify these polynomials by their degree.






Answers 1) 3rd degree 2) 5th degree 3) 1st degree 4) 3rd degree 5) 2nd degree

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Algebra Topics