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
2:24 minutes
Problem 23b
Textbook Question
Textbook QuestionFactor out the greatest common factor from each polynomial. See Example 1. (5r-6)(r+3)-(2r-1)(r+3)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Greatest Common Factor (GCF)
The Greatest Common Factor is the largest integer or algebraic expression that divides two or more terms without leaving a remainder. To find the GCF, one must identify the common factors of the coefficients and the variables in the terms. This concept is essential for simplifying expressions and factoring polynomials effectively.
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Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of its factors, which can include numbers, variables, or other polynomials. This process often simplifies expressions and makes it easier to solve equations. Recognizing patterns, such as the difference of squares or common binomials, is crucial in this step.
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Distributive Property
The Distributive Property states that a(b + c) = ab + ac, allowing one to multiply a single term by each term within a parenthesis. This property is fundamental in expanding expressions and is often used in the process of factoring, as it helps to identify common factors across terms in a polynomial.
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