Published on September 10, 2007
Sullivan Algebra and Trigonometry: Section R.4Polynomials: 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 Slide2: 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. Slide3: Examples of Monomials Slide4: A polynomial in one variable is an algebraic expression of the form Slide5: Example: Coefficients: 2, 0, -3, 1, -5 Degree: 4 Slide6: Polynomials are added and subtracted by combining like terms. Example: Addition Slide7: Example: Subtraction Slide8: Polynomial multiplication can be done by using the distributive property multiple times. Example: Multiplication Slide9: Special Product Formulas Difference of Two Squares Squares of Binomials, or Perfect Squares Slide10: Special Product Formulas Miscellaneous Trinomials Cubes of Binomials, or Perfect Cubes Slide11: Special Product Formulas Difference of Two Cubes Sum of Two Cubes Slide12: 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.