Questions and Answers
What is the result of (fg)(x) where f(x) = 10x - 3 and g(x) = 6x + 8?
-88x³ + 48x² + 88x - 48
What is the result of (fg)(x) where f(x) = 2x - 9 and g(x) = 4x + 5?
8x² - 26x - 45
What is the result of (fg)(x) where f(x) = 5x - 1 and g(x) = 5x + 3?
25x² + 10x - 3
What is the result of (fg)(x) where f(x) = 2x - 3 and g(x) = 4x + 5?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = x - 3 and g(x) = 4x - 2?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = 3x + 7 and g(x) = -2x - 3?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = 5x - 3 and g(x) = x + 1?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = 4x - 7 and g(x) = 9x - 1?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = 6x - 4 and g(x) = x + 6?
Signup and view all the answers
What is the result of (fg)(x) where f(x) = -40b³ + 55b² + 16b - 22?
Signup and view all the answers
Study Notes
Polynomial Expressions
- Polynomials are mathematical expressions involving variables raised to whole number powers.
- Each polynomial is composed of terms that include coefficients, variables, and exponents.
- Degree of a polynomial is determined by the highest power of the variable present.
Examples of Polynomial Forms
- -88x³ + 48x² + 88x - 48: A cubic polynomial with coefficients -88, 48, 88, and -48.
- -35k³ + 70k² + 15k - 30: Another cubic polynomial whose terms reflect similar structures.
- 32m³ - 16m² + 24m - 12: This polynomial has a cubic term, a quadratic term, a linear term, and a constant.
- 20x³ - 18x² - 50x + 45: Features a cubic term that dominates the polynomial, highlighting its non-linear nature.
- -40b³ + 55b² + 16b - 22: A cubic polynomial that illustrates a variety of coefficients.
- 45r³ + 50r² + 63r + 70: Exhibits a positive leading term, indicating growth behavior as r increases.
Function Multiplication
- Functions can be multiplied together to create a new polynomial expression representing their combined behavior.
- Example f(x) = 10x - 3 and g(x) = 6x + 8 leads to (fg)(x) = 60x² + 62x - 24.
- Example f(x) = 2x - 9 and g(x) = 4x + 5 results in (fg)(x) = 8x² - 26x - 45.
Additional Function Combinations
- (fg)(x) for polynomials like f(x) = 5x - 1 and g(x) = 5x + 3 yields 25x² + 10x - 3.
- Combining f(x) = 2x - 3 and g(x) = 4x + 5 gives (fg)(x) = 8x² - 2x - 15, showing interaction between linear terms.
- Each combination reflects how changing coefficients influences the final product.
Evaluating Function Products
- Determining (fg)(x) involves applying distribution across the terms in f(x) and g(x).
- Understanding polynomial multiplication is critical for grasping advanced algebra concepts.
- Each resultant polynomial showcases a unique combination of structural components from the original functions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of the multiplication of functions with these flashcards. Each card presents a polynomial expression for you to analyze. Challenge yourself to identify the product of given functions and expand your mathematical skills.
