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
4:12 minutes
Problem 71c
Textbook Question
Textbook QuestionIn Exercises 69–78, factor each polynomial. x³ − 5 + 4x³y − 20y
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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 simpler components, or factors. This process is essential for simplifying expressions, solving equations, and analyzing polynomial behavior. Common methods include factoring out the greatest common factor (GCF), using special products like the difference of squares, and applying techniques such as grouping.
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Greatest Common Factor (GCF)
The greatest common factor (GCF) of a polynomial is the largest polynomial that divides all terms of the polynomial without leaving a remainder. Identifying the GCF is often the first step in factoring, as it allows for simplification of the polynomial. For example, in the polynomial x³ + 4x³y - 5 - 20y, the GCF can help isolate common terms for easier factoring.
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Grouping Method
The grouping method is a technique used to factor polynomials with four or more terms by grouping terms into pairs or sets that share a common factor. This method simplifies the polynomial into a form that can be factored further. For instance, in the polynomial x³ + 4x³y - 5 - 20y, grouping the terms strategically can reveal common factors that facilitate the factoring process.
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