Factoring Expressions and GCF

The video tutorial explains how to factor a polynomial expression by identifying the greatest common factor (GCF) of its terms. It begins with an introduction to the problem and proceeds to find the GCF by examining the coefficients and the degrees of x and y. The tutorial then demonstrates the factoring process step-by-step, including how to undistribute the GCF from each term. Finally, it concludes with tips for performing these steps more efficiently in the future, emphasizing the use of the distributive property to verify the results.

What is the first step in factoring the expression 4x^4y - 8x^3y - 2x^2?

• Identify the greatest common factor of the coefficients.

• Rewrite the expression in terms of y.

• Add all the terms together.

• Divide each term by 2.

Which number is the greatest common factor of the coefficients 4, 8, and 2?

• 1

• 4

• 8

• 2

What is the greatest degree of x that can be factored out from all terms in the expression?

• x^3

• x^4

• x^2

• x

After factoring out the greatest common factor, what is the expression for the first term 4x^4y?

• 2x^2 * 2x^2y

• 2x^2 * 2x^2

• 2x^2y

• 2x^2 * 4xy

What does the expression 8x^3y become after factoring out 2x^2?

• 4x^2y

• 8xy

• 4xy

• 2x^2y

What is the simplified form of the expression after factoring out 2x^2?

• 2x^2(2x^2y - 4xy + 1)

• 2x^2(2x^2y - 4x^2y - 1)

• 2x^2(2x^3y - 4xy - 1)

• 2x^2(2x^2y - 4xy - 1)

What is the purpose of using the distributive property in this context?

• To divide the terms by 2.

• To verify the factored expression.

• To add the terms together.

• To multiply the terms by x.

What is a key takeaway for factoring expressions more efficiently in the future?

• Always factor out the smallest number.

• Focus on the coefficients only.

• Practice doing steps mentally.

• Ignore the variable y.

Why is it important to understand each step in the factoring process?

• To memorize the steps.

• To factor only simple expressions.

• To apply the process to different problems.

• To avoid using the distributive property.

What should you do if a term in the expression does not contain a variable present in other terms?

• Add a variable to the term.

• Do not factor that variable.

• Factor it out anyway.

• Ignore the term.