Questions and Answers
What is the formula used to calculate the volume of a cereal box?
V = lwh
What is the formula used to calculate the volume of a soda can?
V = πr^2h
What is a polynomial?
A polynomial is an algebraic expression consisting of variables that can be added, subtracted, multiplied, and divided.
Name two operations with variables that cannot exist in a polynomial.
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How are polynomials categorized by the number of terms?
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What determines the degree of a polynomial with one variable?
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What is the standard way to write a polynomial?
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What is the degree of the polynomial 3x - 4?
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What is the degree of the polynomial -x^2 + 2x - 1?
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What does the degree of a polynomial indicate about its graph?
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What should you pay close attention to when rearranging terms in a polynomial?
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Classify the polynomial -6x^5 + 4x^3 + 3x^2 + 11.
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What is the result of writing the expression -2x^2(-5x^2 + 4x^3)?
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Consider the leading term of the polynomial function 2x^7 - 8x^6 - 3x^5 - 3. What is the end behavior?
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How many turning points are there for the graph of y = 2x - x^3?
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What is the degree of the polynomial that generates the given data? x: -6 / -3 / 0 / 3 / 6; y: 846 / 108 / 0 / -126 / -918.
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Study Notes
Polynomial Functions Overview
- Volume formulas such as V = lwh for boxes and V = πr²h for cans are polynomial equations.
Definition and Operations
- A polynomial is an algebraic expression made of variables combined through addition, subtraction, multiplication, and division.
- Polynomials must not have variables in denominators or under radical symbols.
Classification of Polynomials
- Polynomials are classified by the number of terms:
- Monomial: one term
- Binomial: two terms
- Trinomial: three terms
- Classification also occurs by degree, determined by the highest exponent:
- Linear polynomials have degree 1.
- Quadratic polynomials have degree 2.
Standard Form
- Polynomials should be written in descending order of exponents.
- The degree of a polynomial indicates the influence of the term with the largest power on the graph.
Example Exponents and Degrees
- The polynomial 3x - 4 has a degree of 1 (greatest exponent is 1).
- The polynomial -x² + 2x - 1 has a degree of 2 (greatest exponent is 2).
Graph Characteristics
- The degree of a polynomial affects graph shape, including the number of turning points and end behavior.
- Turning points are where the graph changes direction; e.g., the vertex of a parabola.
- End behavior indicates the direction the graph extends towards infinity.
Rearranging Terms
- When creating a standard polynomial form, maintain the sign of each term; negatives must stay with their respective terms.
Polynomial Classifications and Calculations
- The polynomial -6x^5 + 4x^3 + 3x^2 + 11 is classified as quintic.
- Expanding -2x²(-5x² + 4x³) results in -8x^5 - 10x^4.
End Behavior in Graphs
- The leading term of 2x^7 in the polynomial indicates down and up end behavior, reflecting that n is odd and a is positive.
Turning Points in Graphs
- The function y = 2x - x³ exhibits two turning points, with the first point decreasing and the second point increasing.
Degree from Data
- Given the data points, the degree of the polynomial that fits is cubic.
Studying That Suits You
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Description
Test your knowledge of polynomial functions with these flashcards from Algebra 2B Lesson 1, Unit 1. Each card covers essential concepts and formulas that are fundamental to understanding polynomials. Perfect for quick revision or exam preparation.
