Factoring Cubes and Common Factors

The video tutorial covers the process of factoring a sum or difference of cubes, emphasizing the need to memorize specific formulas. It explains the verification of these formulas through division and provides examples of factoring problems, including identifying common factors. The tutorial highlights the importance of recognizing perfect cubes and applying the correct formulas to factor expressions into a binomial and a trinomial.

What is a key difference between factoring cubes and squares?

• Both cubes and squares can only be a difference.

• Cubes must be a difference, while squares can be a sum or difference.

• Both cubes and squares can only be a sum.

• Cubes can be a sum or difference, while squares must be a difference.

What is the result when dividing a sum of cubes by A + B?

• A squared plus AB plus B squared

• A squared minus AB minus B squared

• A squared minus AB plus B squared

• A squared plus AB minus B squared

What is the final step in verifying the sum of cubes formula?

• Multiply the factors

• Ensure the remainder is zero

• Subtract the terms

• Add the opposites

In the example of factoring X cubed minus 27, what is the value of B?

• X

• 9

• 27

• 3

What is the binomial factor when factoring X cubed minus 27?

• X - 27

• X + 3

• X - 3

• X + 27

What is the trinomial factor when factoring X cubed minus 27?

• X squared - 3X + 9

• X squared + 3X - 9

• X squared + 3X + 9

• X squared - 3X - 9

What is the value of B squared in the trinomial factor of X cubed minus 27?

• 27

• 3

• 81

• 9

What is the first step in any factoring problem?

• Identify the sum or difference of cubes

• Look for the greatest common factor

• Apply the quadratic formula

• Perform polynomial long division

When factoring 5X cubed plus 575, what is the common factor?

• 575

• 5

• 125

• X

What should you do if a term does not have three equal factors?

• Perform polynomial long division

• Use the quadratic formula

• Factor out the greatest common factor

• Ignore the term