Learning Outcomes
By the end of this lesson, you will be able to:
- Evaluate a polynomial using the Remainder Theorem.
- Use the Rational Zero Theorem to find rational zeros.
- Use the Factor Theorem to solve a polynomial equation.
- Use synthetic division to find the zeros of a polynomial function.
- Use the Fundamental Theorem of Algebra to find complex zeros of a polynomial function.
- Use the Linear Factorization Theorem to find polynomials with given zeros.
- Use Descartes’ Rule of Signs to determine the maximum number of possible real zeros of a polynomial function.
- Solve real-world applications of polynomial equations.
A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the volume of a small cake to be 351 cubic inches. The cake is in the shape of a rectangular solid. They want the length of the cake to be four inches longer than the width of the cake and the height of the cake to be one-third of the width. What should the dimensions of the cake pan be?
This problem can be solved by writing a cubic function and solving a cubic equation for the volume of the cake. In this section, we will discuss a variety of tools for writing polynomial functions and solving polynomial equations.