Factoring Polynomials and Cubes

The video tutorial covers the basics of factoring polynomials, including understanding factors and remainders, testing polynomial factors, and various factoring techniques. It explains factoring by grouping and special techniques for factoring sums and differences of cubes. The tutorial provides examples and encourages practice to reinforce learning.

What is the remainder when a number is divided by one of its factors?

• The number itself

• 0

• It depends on the number

• 1

Which method can be used to determine if x - 3 is a factor of a polynomial?

• Integration

• Substitution

• Graphing

• Synthetic division

What is the result of factoring x^2 - 4 using the difference of squares method?

• (x + 2)(x - 2)

• (x - 2)(x - 2)

• (x + 2)(x + 2)

• (x - 2)(x + 4)

What is the first step in factoring by grouping?

• Find the greatest common factor for each group

• Combine all terms

• Multiply all terms

• Add a constant term

When factoring by grouping, what should be common in both groups?

• A common factor

• A coefficient

• A variable

• A constant

What is the acronym used to remember the pattern for factoring sums and differences of cubes?

• SOAP

• BODMAS

• FOIL

• PEMDAS

Which of the following is a perfect cube?

• 20

• 18

• 27

• 16

What is the result of factoring 8y^3 - 27 using the sum and difference of cubes?

• (2y + 3)(4y^2 + 6y + 9)

• (2y - 3)(4y^2 - 6y + 9)

• (2y - 3)(4y^2 + 6y + 9)

• (2y + 3)(4y^2 - 6y + 9)

What is the first step in factoring any polynomial?

• Check for perfect cubes

• Find the greatest common factor

• Use synthetic division

• Apply the difference of squares

What is the result of factoring x^3 + 8 using the sum of cubes?

• (x - 2)(x^2 - 2x + 4)

• (x + 2)(x^2 + 2x + 4)

• (x - 2)(x^2 + 2x + 4)

• (x + 2)(x^2 - 2x + 4)