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
4:28 minutes
Problem 93a
Textbook Question
Textbook QuestionFactor each polynomial completely. See Example 6. t⁴ - 1
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Polynomials
Factoring polynomials involves expressing a polynomial as a product of its simpler components, or factors. This process is essential for simplifying expressions and solving equations. Common techniques include identifying common factors, using the difference of squares, and applying special product formulas. For example, the polynomial t⁴ - 1 can be factored using the difference of squares method.
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Difference of Squares
The difference of squares is a specific algebraic identity that states a² - b² = (a - b)(a + b). This identity is crucial for factoring polynomials that can be expressed in this form. In the case of t⁴ - 1, it can be viewed as (t²)² - (1)², allowing us to apply the difference of squares to factor it into (t² - 1)(t² + 1).
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Further Factoring
After applying initial factoring techniques, further factoring may be necessary to completely factor a polynomial. For instance, the factor t² - 1 from the previous example can be further factored as (t - 1)(t + 1). Recognizing when a polynomial can be factored further is key to achieving the complete factorization of the original expression.
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