Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Solving Linear Equations
3:22 minutes
Problem 9a
Textbook Question
Textbook QuestionCONCEPT PREVIEW Which of the following is the correct factorization of x⁴ - 1? A. (x² - 1) (x² + 1) B. (x² + 1) (x + 1) (x - 1) C. (x² - 1)² D. (x - 1)² (x + 1)²
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Difference of Squares
The difference of squares is a fundamental algebraic identity stating that a² - b² can be factored into (a - b)(a + b). This concept is crucial for factoring expressions like x⁴ - 1, as it can be recognized as a difference of squares where a = x² and b = 1.
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Factoring Quadratics
Factoring quadratics involves rewriting a quadratic expression in the form ax² + bx + c as a product of two binomials. In the context of the question, recognizing that x² - 1 can be factored further into (x - 1)(x + 1) is essential for simplifying the expression correctly.
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Polynomial Degree and Roots
The degree of a polynomial indicates the highest power of the variable, which in this case is 4 for x⁴ - 1. Understanding the roots of the polynomial, which are the values of x that make the polynomial equal to zero, helps in determining the correct factorization, as each root corresponds to a linear factor.
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