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
2:18 minutes
Problem 41a
Textbook Question
Textbook QuestionIn Exercises 35–44, factor the greatest common binomial factor from each polynomial. 4x²(3x−1) + 3x − 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 breaking down a polynomial into simpler components, or factors, that when multiplied together yield the original polynomial. This process is essential for simplifying expressions and solving equations. In this case, recognizing common factors within the polynomial helps in rewriting it in a more manageable form.
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Greatest Common Factor (GCF)
The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder. In polynomial expressions, identifying the GCF allows for the extraction of common terms, simplifying the polynomial and making it easier to work with. This is crucial for factoring out the common binomial factor in the given expression.
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Binomial Expressions
A binomial expression is a polynomial that consists of exactly two terms, which can be separated by addition or subtraction. Understanding binomials is important for factoring, as they often represent the simplest form of polynomials. In the context of the given problem, recognizing the binomial factor is key to simplifying the polynomial expression effectively.
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