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
9:07 minutes
Problem 47f
Textbook Question
Textbook QuestionMultiply or divide, as indicated. (xz - xw + 2yz - 2yw)/(z^2 - w^2) * (4z + 4w + xz + wx)/(16 - x^2)
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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 as a product of its factors. This is essential for simplifying expressions, especially when dealing with rational functions. For example, the difference of squares, such as z^2 - w^2, can be factored into (z - w)(z + w), which helps in reducing complex fractions.
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Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including multiplying and dividing them, is crucial for solving algebraic problems. Simplifying rational expressions often requires factoring and canceling common factors to arrive at a more manageable form.
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Rationalizing Denominators
Common Denominators
Finding a common denominator is a key step when adding or subtracting rational expressions. In multiplication and division, while it is not necessary to find a common denominator, recognizing the denominators' structure can aid in simplification. This concept is vital for ensuring that the final expression is in its simplest form after operations are performed.
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