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
Problem 24bBlitzer - 8th Edition
Textbook Question
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 2x^2+5x−3
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Identify the trinomial: .
Look for two numbers that multiply to and add to .
The numbers are and because and .
Rewrite the middle term using these numbers: .
Factor by grouping: and factor out the common factors.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Trinomials
Factoring trinomials involves rewriting a quadratic expression in the form ax^2 + bx + c as a product of two binomials. This process requires identifying two numbers that multiply to ac (the product of a and c) and add to b. Understanding this concept is essential for simplifying expressions and solving equations.
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Prime Trinomials
A trinomial is considered prime if it cannot be factored into the product of two binomials with rational coefficients. Recognizing prime trinomials is crucial because it helps determine whether a quadratic expression can be simplified further or if it remains in its original form. This concept is important for accurately classifying quadratic expressions.
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Quadratic Formula
The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides a method for finding the roots of a quadratic equation. While not directly related to factoring, it serves as a backup method to determine if a trinomial can be factored by revealing the nature of its roots. Understanding this formula is vital for solving quadratic equations when factoring is not feasible.
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Master Introduction to Factoring Polynomials with a bite sized video explanation from Patrick Ford
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Related Practice
Textbook Question
In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.
x² - 4
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