Factoring and Cubes Concepts

This video tutorial covers the factoring of polynomials under special conditions, including the difference and sum of cubes, and polynomials in quadratic form. It explains perfect squares and cubes, providing examples and formulas for the sum and difference of cubes. The video also demonstrates how to apply these formulas to solve problems, discusses the quadratic form and difference of squares, and shows how to factor using the greatest common factor (GCF).

Which of the following is NOT a special condition for factoring polynomials discussed in the video?

• Sum of Squares

• Difference of Squares

• Sum of Cubes

• Difference of Cubes

What is the cube of 3?

• 81

• 18

• 27

• 9

Which formula is used for factoring the sum of cubes?

• a - b(a^2 + ab + b^2)

• a^2 - ab + b^2

• a^2 + ab + b^2

• a + b(a^2 - ab + b^2)

In the sum of cubes formula, what is the first step after identifying A and B?

• Subtract B from A

• Add A and B

• Multiply A and B

• Square A

What is the first sign in the formula for the difference of cubes?

• Plus

• Divide

• Minus

• Multiply

When factoring a sum of cubes, what sign does the formula start with?

• Divide

• Multiply

• Minus

• Plus

In a complex sum of cubes problem, what is the cube root of 64?

• 2

• 4

• 8

• 16

What is the first step in factoring a quadratic polynomial?

• Identify the GCF

• Add the terms

• Square the terms

• Write two sets of parentheses

What is the result of factoring x^2 - 9?

• (x - 3)^2

• (x + 3)^2

• (x + 9)(x - 9)

• (x + 3)(x - 3)

What is the greatest common factor (GCF) in the example problem discussed?

• 6

• 4

• 2

• 8