3.5 Polynomial Functions

The function shown has:

• Degree two with negative leading coefficient.

• Degree three with negative leading coefficient.

• Degree four with negative leading coefficient.

• Degree four with positive leading coefficient.

Which of the following could be a possible equation for the function shown?

• f(x) =-2x³ + x² - 5x + 1

• f(x) = 2x³ - 4x² + x + 1

• f(x) = 3x² + 5x + 1

• f(x) = -2x³ +3x - 1

State the minimum degree of the function shown:

• 3

• 4

• 5

• 6

Select all the graphs which show even degree functions.

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• 
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Which of the following functions could represent the graph shown?

• f(x) = -2x⁵

• f(x) = -2x⁴ + 7x³ + 3x² -5x + 8

• f(x) = 2x⁵ + 3x⁴ - 3x³ + 5x² - 3x + 4

• None of these functions could represent the graph shown.

Which description best matches the function shown:

• Odd degree with positive leading coefficient.

• Even degree with positive leading coefficient.

• Degree three, with negative leading coefficient.

• Degree four, with negative leading coefficient.

What is k in the given synthetic division pattern?

What are the zeros of the polynomial function

 $P\left(x\right)=x\left(x-1\right)\left(x+2\right)\left(x-3\right)$  ?

• 1, 2, 3

• 0, 1, 2, 3

• 0, -1, 2, -3

• 0, 1, -2, 3

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)
• f(x) = (x-4)(x+1)²(x+2)(x+4)
• f(x) = (x-4)(x-1)²(x-2)(x+4)
• f(x) = (x+4)(x+1)²(x-2)(x-4)

The polynomial is...

• Odd degree, positive leading coefficient.
• Odd degree, negative leading coefficient.
• Even degree, positive leading coefficient.
• Even degree, negative leading coefficient.