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:
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