1. Sullivan Algebra and Trigonometry: Section R.4 Polynomials Objectives of this Section Recognize Monomials Recognize Polynomials Add, Subtract, and Multiply Polynomials Know Formulas for Special Products

2. A monomial in one variable is the product of a constant times a variable raised to a nonnegative integer power. Thus, a monomial is of the form: where a is a constant, x is a variable, and k > 0 is an integer.

3. Monomial Coefficient Degree 34 1 -9 0 Examples of Monomials

4. A polynomial in one variable is an algebraic expression of the form

5. Example: Coefficients: 2, 0, -3, 1, -5 Degree: 4

6. Polynomials are added and subtracted by combining like terms. Example: Addition

7. Example: Subtraction

8. Polynomial multiplication can be done by using the distributive property multiple times. Example: Multiplication

9. Special Product Formulas Difference of Two Squares Squares of Binomials, or Perfect Squares

10. Special Product Formulas Miscellaneous Trinomials Cubes of Binomials, or Perfect Cubes

11. Special Product Formulas Difference of Two Cubes Sum of Two Cubes

12. Polynomials in Two Variables The degree of a polynomial in two variables is the highest degree of all the monomials with nonzero coefficients. The degree of each monomial is the sum of the powers of the variables. 4 5 5DegreePolynomial