Factoring Polynomials and Cubes

The video tutorial covers factoring techniques for sums and differences of cubes. It begins with an introduction to the topic, followed by two detailed examples. The first example demonstrates factoring a difference of cubes, while the second example focuses on a sum of cubes. Each example emphasizes the importance of factoring out the greatest common factor first. The video concludes with a summary and helpful tips for factoring.

What is the first step in factoring any polynomial?

• Recognize the difference of squares

• Simplify the expression

• Identify the sum of cubes

• Factor out the greatest common factor

In the expression 4x^3 - 32, what is the greatest common factor?

• 4

• x

• 8

• 2

When factoring a difference of cubes, what is the form of the binomial factor?

• A - B

• A^2 + AB + B^2

• A^2 - AB + B^2

• A + B

In the expression x^3 - 8, what is the value of A?

• x

• 2

• 4

• 8

In the expression 2x^3 + 250, what is the greatest common factor?

• 5

• 10

• 25

• 2

What is the value of B in the expression x^3 + 125?

• 4

• 3

• 5

• 6

What is the form of the trinomial factor when factoring a sum of cubes?

• A^2 - AB - B^2

• A^2 - AB + B^2

• A^2 + AB + B^2

• A^2 + AB - B^2

What is the result of B squared if B equals 5?

• 15

• 25

• 10

• 20

Which of the following expressions is a sum of cubes?

• x^3 + 27

• x^3 - 27

• x^3 - 64

• x^3 + 64

What is the binomial factor of the expression x^3 + 125?

• x - 5

• x + 5

• x + 25

• x - 25