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Chapter 1: Preliminary Information

This chapter provides a foundational understanding of polynomials in algebra. It explains what constitutes a polynomial, emphasizing operations restricted to addition, subtraction, and multiplication of variables. The chapter also highlights the concept of terms and factors within expressions, offering special names according to the number of terms in a polynomial. Furthermore, it discusses the degree of a polynomial as the highest number of variable factors present in any term. Lastly, the chapter introduces the multiplication of binomials using the FOIL method.

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Chapter 1: Preliminary Information

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  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. • 3x2 + 5x -7 has three terms. • Special names are used for expressions with a certain number of terms.

  7. Names according to # of terms

  8. Factors • Factors in an expression are parts of the expression that are multiplied together. • 5x2 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

  11. Multiplying Binomials F O I L

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