Solving Polynomial Equations A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Types of Polynomial Equations Type of FunctionDegreeExample Constant Linear Quadratic Cubic Quartic Quintic nth degree polynomial

Solving Polynomial Equations by Factoring

Review  The degree of a polynomial equation tells the number of roots for that equation  Once a polynomial equation is factored to simplest terms, if any terms are quadratic expressions:  Use quadratic formula  Complete the square  Solve using square roots  The degree of a polynomial equation tells the number of roots for that equation  Once a polynomial equation is factored to simplest terms, if any terms are quadratic expressions:  Use quadratic formula  Complete the square  Solve using square roots

Find all zeros of the polynomial function:

Writing Equations of Polynomial Functions

Complex Conjugate Theorem