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.