1. Chapter 1: Preliminary Information Section 1-4: Polynomials

2. Objectives Given an expression: ◦ Tell whether or not it is a polynomial. ◦ If it is, then name it:  By degree  By number of terms Given two binomials, multiply them together.

3. Polynomials Polynomials are algebraic expressions that involve only the operations of addition, subtraction, and multiplication of variables. They involve no non-algebraic operations such as: ◦ Absolute value ◦ Any operation where the real numbers are not a closed set:  Division (because you cannot divide by zero)  Square roots (because you cannot have square roots of negatives)

4. More on Polynomials: The following expressions are examples of polynomials:

5. More on Polynomials The following examples are not polynomials:

6. Terms of an Expression “Terms” in an expression are the parts of the expression that are added or subtracted. 3x 2 + 5x -7 has three terms. Special names are used for expressions with a certain number of terms.

7. Names according to # of terms Number of TermsNameExample 1Monomial3x 2 y 5 2Binomial3x 2 + y 5 3Trinomial3 – x 2 + y 5 4 or moreNo specific name3x 5 - 2x 4 + 5x 3 - 6x 2 + 2x

8. Factors Factors in an expression are parts of the expression that are multiplied together. 5x 2 has three factors: 5, x, and x. Special names are given to polynomials depending on how many variables are multiplied together.

9. Degree of a Polynomial The degree of a polynomial is the maximum number of variables that appear as factors in any one term.

10. Names according to degree DegreeNameExample 0Constant13 1stLinear5x 2ndQuadratic7x 2 3rdCubic4x 3 4thQuarticx4x4 5thQuintic9x 5 6th or moreNo special name3x 17

11. Multiplying Binomials