Zeros and Multiplicity Worksheet
Explore the concepts of zeros and multiplicity in polynomial functions with this comprehensive worksheet for Grade 9 Algebra students.
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Zeros and Multiplicity
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Read each question carefully and provide honest answers. Show your work where applicable.
1. A zero of a polynomial function is a value of x for which f(x) = .
2. The multiplicity of a zero is the number of times its corresponding appears in the factored form of the polynomial.
3. If a zero has an even multiplicity, the graph of the polynomial will the x-axis at that zero.
4. If a zero has an odd multiplicity, the graph of the polynomial will the x-axis at that zero.
5. Which of the following polynomial functions has a zero at x = 2 with a multiplicity of 3?
f(x) = (x-2)(x+1)^2
f(x) = (x+2)^3
f(x) = (x-2)^3(x+1)
f(x) = (x-2)^2(x+3)
6. A polynomial has zeros at x = -1 (multiplicity 2) and x = 3 (multiplicity 1). What is the degree of the polynomial?
1
2
3
4
7. For the polynomial function f(x) = (x-4)^2(x+5), identify the zeros and their multiplicities.
8. Write a polynomial function in factored form with zeros at x = 0 (multiplicity 1), x = 1 (multiplicity 2), and x = -3 (multiplicity 1).
9. If a polynomial has a zero with an odd multiplicity, the graph will cross the x-axis at that zero.
True
False
10. The degree of a polynomial is always equal to the number of distinct zeros.
True
False
11. Analyze the graph of the polynomial function shown below. Identify the zeros and their multiplicities.