Chapter 1: Preliminary Information Section 1-4: Polynomials

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.

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)

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

More on Polynomials The following examples are not polynomials:

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.

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

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.

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

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

Multiplying Binomials