Exploring Polynomial Functions and Their Roots

What are the zeros of the polynomial X^3 - 3X^2 - 4X + 12?

• 3, 2, -1

• 3, -2, 2

• 1, -2, 3

• 2, -3, 1

Which of the following is a factor of the polynomial X^3 - 4X^2 - 5X?

• X - 3

• X + 2

• X + 1

• X - 5

What is the root of the polynomial X^4 + 7X^3 + 13X^2 + 3X + 18 found using Desmos?

• -1

• -2

• 2

• 1

What is the effect of the transformation Y = -2X^3 - 7 on the graph of the parent function Y = X^3?

• Reflected over the X-axis and shifted up

• Shifted down and vertically compressed

• Reflected over the X-axis and shifted down

• Shifted up and vertically stretched

How does the graph of Y = X^3 + 5 differ from the graph of Y = X^3?

• Shifted up by 5 units

• Shifted down by 5 units

• Shifted left by 5 units

• Shifted right by 5 units

What is the remainder when the polynomial 2X^4 + 3X^3 - X^2 - 2 is divided by X - 2 using synthetic substitution?

• -2

• 2

• 4

• 0

Which quadrant does the graph of Y = 3 - X - 4 appear in?

• Quadrant 3 and 4

• Quadrant 1 and 4

• Quadrant 2 and 3

• Quadrant 1 and 2

What are the factors of the polynomial X^3 - 6X^2 + 4X - 24 using grouping?

• (X - 6)(X^2 - 4)

• (X - 4)(X^2 + 6)

• (X - 6)(X^2 + 4)

• (X - 4)(X^2 - 6)

What is the solution to the equation √(3X - 8) = 4?

• X = 4

• X = 8

• X = 16

• X = 12

What is the transformation that takes place in the function G(X) = 2F(X - 4) + 6?

• Shifted up 6 units and right 4 units

• Shifted down 6 units and left 4 units

• Shifted down 6 units and right 4 units

• Shifted up 6 units and left 4 units