About This Chapter
Polynomial Equations in Precalculus - Chapter Summary
Our experienced instructors will define and explain a host of theorems as you progress through this precalculus math chapter, including the division, remainder and factor theorems. Explore roots in precalculus and learn to use the root location, conjugate radical roots and complex conjugate roots theorems.
After viewing each of the lessons in this chapter, you will have worked with the following precalculus principles:
- Remainder and factor theorems
- Calculating derivatives of polynomials
- Fundamental theorem of algebra
- Rational roots theorem
- Sum-to-product identities
Master precalculus math quickly and easily. Our expert instructors present each topic in an engaging video lesson - view it as many times as you like while you study. The lesson transcripts are a great way to review formulas and terminology, and you can confirm your progress by taking the optional quizzes and chapter exam. Should you have any questions as you study, just ask. You'll have polynomial equations mastered in no time!
1. Remainder Theorem & Factor Theorem: Definition & Examples
In this lesson, you will learn about the remainder theorem and the factor theorem. You will also learn how to use these theorems to find remainders and factors of polynomials.
2. Calculating Derivatives of Polynomial Equations
Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.
3. Fundamental Theorem of Algebra: Explanation and Example
In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.
4. How to Use the Rational Roots Theorem: Process & Examples
When it comes to solving polynomials, it can sometimes be easier to begin with a list of possible solutions to try. This video lesson tells you how to form a list of possible solutions by using the rational roots theorem.
5. Sum-to-Product Identities: Uses & Applications
In this video lesson, you will learn about the four sum-to-product identities for the sine and cosine functions. Learn how to go from the sum or subtraction of two functions to the product of two functions along with the two angles.
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Other chapters within the GRE Math: Study Guide & Test Prep course
- Functions in Precalculus
- Analytical Geometry in Precalculus
- Logarithms & Trigonometry
- Limits of Sequences & Functions
- Calculating Derivatives
- Curve Sketching in Precalculus
- Differentiable Functions & Min-Max Problems
- Indefinite Integrals in Calculus
- Definite Integrals in Calculus
- Additional Topics in Calculus
- L'Hopital's Rule, Integrals & Series in Calculus
- Analytic Geometry in 3-Dimensions
- Partial Derivatives
- Calculus: Min/Max & Integrals
- Algebra: Differential Equations
- Algebra: Matrices & Vectors
- Algebra: Determinants & Transformations
- Algebra: Number Theory & Abstract Algebra
- Additional Topics: Sets
- Additional Topics: Unions & Intersections
- Additional Topics: Graphing & Probability
- Additional Topics: Standard Deviation
- Additional Topics: Topology & Complex Variables
- Additional Topics: Trigonometry
- Additional Topics: Theorems, Analysis & Optimizing
- GRE Math Flashcards