Characteristics of Polynomials
Explore the key characteristics of polynomial functions, including degree, leading coefficient, end behavior, and roots.
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Characteristics of Polynomials
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. The of a polynomial is the highest exponent of the variable in the polynomial.
2. The is the coefficient of the term with the highest degree.
3. A polynomial with a degree of 2 is called a .
4. The of a polynomial describes the behavior of the graph of the polynomial as x approaches positive or negative infinity.
1. Which of the following is NOT a polynomial function?
f(x) = 3x^2 - 2x + 1
f(x) = 4x^3 + 5x^-1
f(x) = 7x^4
f(x) = 2x + 9
2. What is the degree of the polynomial P(x) = 5x^4 - 2x^7 + 3x - 1?
4
5
7
1
1. Describe the end behavior of a polynomial function with an odd degree and a positive leading coefficient.
2. Consider the polynomial function f(x) = -2x^3 + 5x^2 - x + 8. Identify its degree and leading coefficient.
For the graph below, determine the possible degree of the polynomial and whether the leading coefficient is positive or negative.