# 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, 4x^{2}.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:**5x**^{2}**-4x** - A
**trinomial**has three terms. For example:**3y**^{2}**+5y****-2** - Any polynomial with four or more terms is just called a polynomial. For example:
**2y**^{5}**+ 7y**^{3}**- 5y**^{2}**+9y****-2**
Practice classifying these polynomials by the number of terms: 1. 5y 2. 3x ^{2}-3x+1 3. 5y-10 4. 8xy 5. 3x ^{4}+x^{2}-5x+9 Answers: 1) Monomial 2) Trinomial 3) Binomial 4) Monomial 5) Polynomial2. Degree. The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s).Examples: - 5x
^{2}-2x+1 The highest exponent is the 2 so this is a 2^{nd}degree trinomial. - 3x
^{4}+4x^{2}The highest exponent is the 4 so this is a 4^{th}degree binomial. - 8x-1 While it appears there is no exponent, the x has an understood exponent of 1; therefore, this is a 1
^{st}degree binomial. - 5 There is no variable at all. Therefore, this is a 0 degree monomial. It is 0 degree because x
^{0}=1. So technically, 5 could be written as 5x^{0}. - 3x
^{2}y^{5}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 7^{th}degree monomial.
Classify these polynomials by their degree. 1.7x ^{3}+5^{2}+12.6y ^{5}+9y^{2}-3y+83.8x-4 4.9x ^{2}y+35.12x ^{2}Answers 1) 3^{rd} degree 2) 5^{th} degree 3) 1^{st} degree 4) 3^{rd} degree 5) 2^{nd} degree |

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