Factoring with the Greatest Common Factor

The video tutorial explains how to factor polynomials by identifying and extracting the greatest common factor (GCF) from each term. It provides a detailed example to illustrate the process and emphasizes the importance of starting with the GCF to simplify polynomial expressions. The tutorial concludes with a final example and encourages viewers to practice this technique for easier problem-solving.

What is the first step in factoring polynomials?

• Divide by the highest coefficient

• Combine like terms

• Expand the polynomial

• Identify the greatest common factor

In the polynomial 4x^3y^3 + 8x^4y^3 - 12x^2y^4, what is the greatest common factor?

• 2x^2y^2

• 4x^3y^3

• 4x^2y^3

• 8x^4y^4

When factoring out the greatest common factor, what should you do if the terms have different numbers of variables?

• Factor out the variable with the lowest exponent

• Factor out the variable with the highest exponent

• Factor out the sum of the exponents

• Ignore the variables

What is the result of factoring 4x^3y^3 + 8x^4y^3 - 12x^2y^4 by the greatest common factor?

• 4x^2y^3(x + 2x^2 - 3y^2)

• 4x^2y^3(x + 2x - 3y)

• 4x^2y^3(x + 2x^2 - 3y)

• 4x^2y^3(x + 2x^2 - 3xy)

Why is it important to use the distributive property when factoring?

• To expand the polynomial

• To combine like terms

• To verify the factorization is correct

• To ensure the polynomial is simplified

What happens if you forget to include the addition or subtraction signs when factoring?

• The factorization will be incorrect

• The polynomial will be simplified

• The polynomial will be expanded

• The terms will be combined

In the example 3aB^2 - 6a^2B^3, what is the greatest common factor?

• 6a^2B^3

• 3a^2B^3

• aB

• 3aB^2

What should you write if you factor out everything from a term?

• 0

• 1

• The original term

• The greatest common factor

What is the purpose of factoring out the greatest common factor first?

• To change the polynomial's degree

• To make the polynomial more complex

• To simplify the polynomial

• To eliminate variables

What should you always check after factoring out the greatest common factor?

• If the polynomial can be factored further

• If the polynomial is expanded

• If the polynomial is combined

• If the polynomial is divided