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Characteristics of Polynomials

Explore the key characteristics of polynomial functions, including degree, leading coefficient, end behavior, and roots.

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Grade 10 Math AlgebraCharacteristics of Polynomials
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Fill in the BlanksMultiple ChoiceShort AnswerCustom

Standards

CCSS.MATH.CONTENT.HSA.APR.B.3CCSS.MATH.CONTENT.HSA.CED.A.2
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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?

a

f(x) = 3x^2 - 2x + 1

b

f(x) = 4x^3 + 5x^-1

c

f(x) = 7x^4

d

f(x) = 2x + 9

2. What is the degree of the polynomial P(x) = 5x^4 - 2x^7 + 3x - 1?

a

4

b

5

c

7

d

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.

xy

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