1. Lesson 7-4 Polynomials
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2. Some Definitions Polynomial – a monomial or a sum of monomials
Binomial – the sum of two monomials
Trinomial – the sum of three monomials
Remember that subtraction can be written as addition of a negative, So polynomials can also be the subtraction of monomials.

3. Examples
State whether each expression is a polynomial. If it is a polynomial, specify which kind.

4. Example Write a polynomial to represent the area of the shaded region.
Shaded region = Rectangle – Circle

5. Problems to Try
State whether each expression is a polynomial. If yes, which kind?
5. Write a polynomial to represent the area of the shaded region.

6. More Definitions
Degree of a Monomial – The sum of all the exponents of the variables in the monomial
Degree of a Polynomial – The largest degree of any of the monomials in the polynomial.

7. Examples
Find the degree of each monomial

8. Examples Find the degree of each polynomial 1. Identify each monomial
2. Find the degree of each monomial
3. The largest degree is your answer

9. Problems to Try
Find the degree of the polynomial. 1. 2. 3.

10. Standard Form of a Polynomial
To be in standard form, put the terms of the polynomial in order so that the exponents go from greatest to least.
Ex.
Standard Form
-2 is called the leading coefficient because it is the coefficient of the largest power.