Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Factoring Polynomials
5:19 minutes
Problem 42c
Textbook Question
Textbook QuestionIn Exercises 39–44, factor by introducing an appropriate substitution. x⁴ − 4x² − 5
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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 rewriting a polynomial expression as a product of simpler polynomials. This process is essential for solving polynomial equations and simplifying expressions. In the given expression, recognizing patterns or using techniques like grouping can help identify factors.
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Substitution Method
The substitution method is a technique used to simplify complex expressions by replacing a variable with another expression. In this case, substituting x² with a new variable (e.g., y) can transform the quartic polynomial into a quadratic one, making it easier to factor.
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Quadratic Equations
Quadratic equations are polynomial equations of degree two, typically in the form ax² + bx + c = 0. They can be solved using various methods, including factoring, completing the square, or the quadratic formula. Understanding how to factor quadratics is crucial for solving higher-degree polynomials like the one in the question.
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