Key Features of Polynomials

Multiple Choice

Which of the following best describes the standard form of a polynomial?

• All terms are written in descending order according to the exponents.

• All terms are written in ascending order according to the exponents.

• The highest exponent is always zero.

• The coefficients are always positive.

Multiple Select

Which of the following functions is NOT a polynomial?

• h(x) = x⁴ - (1/4)x² + 3

• g(x) = 7x - √3 + πx²

• f(x) = 5x² + 3x^-1 - x

• k(x) = x + 2^x - 0.6x⁵

Multiple Choice

Which of the following statements about the end behavior of polynomials is correct?

• For even degree and positive leading coefficient, both ends go up.

• For odd degree and positive leading coefficient, both ends go down.

• For even degree and negative leading coefficient, both ends go up.

• For odd degree and negative leading coefficient, both ends go up.

Fill in the Blanks

The maximum number of turning points a polynomial of degree n can have is

.

Open Ended

Explain how the degree and leading coefficient of a polynomial affect its end behavior.

Drag and Drop

Given y = -4x² - x - 5, Identify the:

degree​

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type​

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leading coefficient​

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maximum number of turns​

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Drag these tiles and drop them in the correct blank above

2

quadratic

-4

1

-1

-5

quartic

Multiple Choice

Given the polynomial y = -4x² - x - 5, what is the end behavior?

• $$f\left(x\right)\rightarrow\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ as\ x\rightarrow-\infty$$

• $$f\left(x\right)\rightarrow\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow-\infty$$

• $$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ as\ x\rightarrow-\infty$$

• $$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow-\infty$$

Draw

Sketch a graph of y = -4x² - x - 5

Multiple Choice

What is the difference between the degree of a polynomial and its leading coefficient?

• The degree is the highest exponent, while the leading coefficient is the number in front of the variable with the highest exponent.

• The degree is the number in front of the variable, while the leading coefficient is the highest exponent.

• The degree is always 1, while the leading coefficient is always 0.

• The degree and leading coefficient are always the same.