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End Behavior
Volume/Area
Factoring
Types of Zeros
Zeros
100

How can we determine the end behavior of a polynomial algebraically (without using a graph)?

Leading term (degree and coefficient)

100

Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 10 inches wide and 15 inches long, and then folding up the sides. The width of the open-top box, in terms of x, will be represented by this expression.

10-2x

100

Factor x2-12x+36

(x-6)2

100

If polynomial P(x) is known to have a degree of 7, a zero at x = -5 with a multiplicity of 3, a zero at x = 1 with a multiplicity of 2, and a non-real zero, what is the final zero?

Non-real

100

Find the zeros of the function: f(x)=2x(x-4)(x-1)

x = 0, 4, 1
200

Write the end behavior for a polynomial with a positive leading coefficient and an even degree.

x -> -oo, y -> oo

x -> oo, y -> oo

200

Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 12 inches wide and 14 inches long, and then folding up the sides. The volume of the open-top box, in terms of x, will be represented by this expression.

V(x)=(12-2x)(14-2x)(x)

200

Factor 2x2+6x-8

2(x-1)(x+4)

200

How can you determine the number of zeros in a polynomial?

By its degree (highest exponent)

200

List the zeros and their multiplicities from the polynomial. 

y=x(x-3)^3(x+4)^5

x = 0 multiplicity 1

x = 3 multiplicity 3

x = -4 multiplicity 5

300

Describe the end behavior of the polynomial 

g(x) = 4x5-3x3+7x

x -> -oo, y -> -oo

x -> oo, y -> oo

300

Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 10 inches wide and 15 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then what is a reasonable domain for this context?

0<x<5

300

Factor the expression x3-8

(x-2)(x2+2x+4)

300

How do you determine the number of non-real zeros of a polynomial?

Subtract the number of real zeros from the degree

300

Find the zeros of the function:

f(x) = -3(2x-1)(x+6)(3x+7)

x = 1/2, -6, -7/3
400

Describe the end behavior of the polynomial

h(x) = 2x2-5x5+6x3-10

x -> -oo, y -> oo

x -> oo, y -> -oo

400

Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 10 inches wide and 15 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then write an equation to represent the volume of the box.

V(x)= x(10-2x)(15-2x)

400

Factor 2x3+1024

2(x+8)(x2-8x+64)

400

Identify the number of real and non-real zeros of 3x3-3

1 real, 2 non-real

400

Find the zeros of this function: y=2x3+14x2+12x

x = 0, -6, -1

500

Describe the End Behavior of f(x)=-4x4+3x5-x2+7

x -> -oo, y -> -oo

x -> oo, y -> oo

500

Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 10 inches wide and 15 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then what value of x will give her the greatest volume? What is the volume?

x = 1.96

V(x) = 132.03

500

Factor 3x3-648

3(x-6)(x2+6x+36)

500

What is the number and type of roots of x3+2x?

1 real, 2 non-real

500

The zeros of:

3x3 + 30x2 + 63x

x = 0, -3, -7