Introduction to Polynomials Module 3.1 Introduction to Polynomials

Identifying Type of Function Find the pattern or growth rate of the output and then determine the type of function. Linear: There is a common difference and the highest power is equal to 1. Table Example (x + 2) Exponential: There is a common ratio Table Example ( 2 𝑥 ) Quadratic: There is a common second sum Table Example ( 𝑥 2 +5) Cubic: There is a common third sum Table Example (𝑥 3 +5)

Family of Function Matching Sheet on Document Camera

Facts about Polynomials A Polynomial is one or more terms in an equation. There are three unique names for Polynomials:  Monomial: One term. Examples: x, xy², x³yz Binomial: Two terms connected by addition or subtraction. Examples: x + y, 3x²-y Trinomial: Three terms connected by addition or subtraction. Examples: x² + 3x -2 Any Polynomial with more than three terms is just referred to as a Polynomial. Example: 𝑥 4 + x³ - 3x² + 6

More Facts about Polynomial Functions The degree of a monomial can be found by adding up all the exponents. The degree of a Polynomial can be found by taking the degree of the monomial with the highest degree. A function with an even degree will have the end points of a graph always going in the same direction Positive leading coefficient: Both up Negative Leading Coefficient Both down A function with an odd degree will have the end points of a graph always going in opposite directions Positive Leading Cooefficient: Left Down, right up Negative Leading Coefficient, Left Up, right down.

Fundamental Theorem of Algebra Every polynomial equation with degree greater than zero will have at least one root (or zero, or solution) in the set of complex numbers. A polynomial has exactly the number of complex roots(real or imaginary) equal to it’s degree.