Characteristics of Polynomials Worksheet
Explore the characteristics of polynomials including degree, leading coefficient, and end behavior through various exercises.
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Characteristics of Polynomials
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Read each question carefully and provide the best answer. Show all your work where applicable.
1. Which of the following is NOT a polynomial?
$5x^3 - 2x + 1$
$\frac{3}{x} + 2x^2 - 7$
$4x^2 + \sqrt{2}x - 6$
$x^4 - 3x^2 + \frac{1}{2}$
2. What is the degree of the polynomial $P(x) = 7x^5 - 2x^8 + x - 10$?
5
8
1
10
3. The of a polynomial is the highest exponent of the variable in the polynomial.
4. A polynomial with a degree of 2 is called a polynomial.
5. The of a polynomial is the coefficient of the term with the highest degree.
6. For the polynomial $f(x) = -3x^4 + 5x^2 - x + 9$, identify the following:
a) Degree:
b) Leading Coefficient:
c) Constant Term:
7. Describe the end behavior of a polynomial with an odd degree and a positive leading coefficient.
8. The graph of a polynomial function always has at least one x-intercept.
True
False
9. A polynomial of degree 'n' can have at most 'n' real roots.
True
False
10. Sketch a possible graph for a polynomial function with the following characteristics:
- Even degree
- Negative leading coefficient
- Two real roots