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
6:09 minutes
Problem 47d
Textbook Question
Textbook QuestionIn Exercises 23–48, factor completely, or state that the polynomial is prime. x³ - 7x² - x + 7
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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 expressing a polynomial as a product of its simpler polynomial factors. This process is essential for simplifying expressions and solving equations. Techniques include finding common factors, using the distributive property, and applying special factoring formulas such as the difference of squares or perfect square trinomials.
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Rational Root Theorem
The Rational Root Theorem provides a method for identifying possible rational roots of a polynomial equation. It states that any rational solution, expressed as a fraction p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. This theorem is useful for testing potential roots to simplify the polynomial.
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Synthetic Division
Synthetic division is a simplified form of polynomial long division that allows for quicker division of a polynomial by a linear factor. It is particularly useful when applying the Rational Root Theorem to test potential roots. By using synthetic division, one can determine if a polynomial can be factored further or if it is prime.
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