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Why It Matters: Power and Polynomial Functions

Learning Objectives

Characteristics of Power and Polynomial Functions
• Identify power functions.
• Identify end behavior of power functions.
• Identify polynomial functions.
• Identify the degree and leading coefficient of polynomial functions.
• Identify local behavior of polynomial functions.

Graphs of Polynomial Functions

• Identify zeros of polynomial functions with even and odd multiplicity
• Use the degree of a polynomial to determine the number of turning points of its graph
• Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem
• Write the equation of a polynomial function given it’s graph

Divide Polynomials

• Use long division to divide polynomials.
• Use synthetic division to divide polynomials.

Methods for Finding Zeros of Polynomials

• Evaluate a polynomial using the Remainder Theorem.
• Use the Factor Theorem to solve a polynomial equation.
• Use the Rational Zero Theorem to find rational zeros.
• Find zeros of a polynomial function.
• Use the Linear Factorization Theorem to find polynomials with given zeros.
• Use Descartes’ Rule of Signs.
• Solve real-world applications of polynomial equations