Cube Functions and Polynomial Properties

The video tutorial covers solving polynomials by factoring, focusing on methods like sum and difference of cubes, and using the quadratic formula. It explains the grouping method for factoring and applies these concepts to solve word problems. The tutorial provides examples and emphasizes understanding the discriminant in quadratic equations.

What is the cube of 3?

• 27

• 9

• 64

• 81

Which of the following is a correct property of cubes?

• Negative cubed is positive

• Negative cubed is negative

• Positive cubed is zero

• Positive cubed is negative

What is the cube root of 64?

• 2

• 16

• 8

• 4

In the sum of cubes formula, what is the result of (a^3 + b^3)?

• (a + b)(a^2 - ab + b^2)

• (a - b)(a^2 + ab + b^2)

• (a + b)(a^2 + ab + b^2)

• (a - b)(a^2 - ab + b^2)

What is the first step in the grouping method for factoring polynomials?

• Square each term

• Separate the terms into two groups

• Use the quadratic formula

• Find the greatest common factor

What is the greatest common factor of 6x^3 and 8x^2?

• 6x^2

• 2x^2

• 4x

• 2x

What is the result of factoring x^2 - 4?

• (x - 2)(x + 4)

• (x + 2)(x - 2)

• (x - 2)(x - 2)

• (x + 2)(x + 2)

What is the quadratic formula?

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / 2a

What is the volume function V(x) for the cardboard box problem?

• x^3 - 16x^2 + 36x

• x^3 - 6x^2 + 36x

• x^3 - 16x^2 + 63x

• x^3 - 6x^2 + 63x

What is the reasonable domain for the volume function V(x) in the cardboard box problem?

• 0 < x < 9

• 0 ≤ x ≤ 9

• 0 ≤ x ≤ 7

• 0 < x < 7