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
3:09 minutes
Problem 63d
Textbook Question
Textbook QuestionFactor each polynomial. See Examples 5 and 6. 25s^4-9t^2
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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 components, or factors. This process is essential for simplifying expressions, solving equations, and analyzing polynomial behavior. Common methods include finding the greatest common factor, using special products like the difference of squares, and applying the quadratic formula for higher-degree polynomials.
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Difference of Squares
The difference of squares is a specific factoring technique applicable to expressions of the form a^2 - b^2, which can be factored into (a + b)(a - b). In the given polynomial, 25s^4 - 9t^2 can be recognized as a difference of squares, where 25s^4 is (5s^2)^2 and 9t^2 is (3t)^2. This recognition allows for straightforward factoring.
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Exponents and Polynomial Terms
Understanding exponents is crucial in polynomial expressions, as they indicate the power to which a variable is raised. In the polynomial 25s^4 - 9t^2, the term 25s^4 signifies that s is raised to the fourth power, while 9t^2 indicates t is squared. Recognizing these terms helps in applying appropriate factoring techniques and understanding the polynomial's structure.
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