Dividing and Factoring Expressions

The video tutorial explains how to factor an algebraic expression by identifying and using the greatest common factor (GCF). It begins with an introduction to the concept of factoring, followed by identifying the GCF in both numbers and variables. The tutorial then provides a step-by-step guide to factoring the expression, highlighting common mistakes students make, such as omitting terms that are the GCF. The importance of including all terms to ensure the expression is complete is emphasized.

What is the first step in factoring an algebraic expression?

• Add all coefficients

• Multiply all terms

• Identify the greatest common factor

• Divide by the smallest coefficient

What is the purpose of factoring an algebraic expression?

• To simplify the expression

• To make it more complex

• To change the variables

• To add more terms

What is the greatest common factor of the numbers 14, 21, and 7?

• 21

• 14

• 7

• 3

Which of the following is the greatest common factor of y^3, y^2, and y?

• 1

• y^2

• y^3

• y

What is the smallest exponent among y^3, y^2, and y?

• 0

• 2

• 3

• 1

After factoring out 7y from 14y^3, what is the remaining term?

• y^3

• 7y^2

• 14y^2

• 2y^2

What is the result of dividing -21y^2 by 7y?

• -7y

• -3y

• -21y

• -3y^2

What is the result of dividing 7y by 7y?

• 1

• 7

• 0

• y

What is the result of factoring 14y^3 - 21y^2 + 7y by 7y?

• 2y^3 - 3y^2 + 1

• 2y^2 - 3y + 1

• 2y^2 - 3y + 7

• 14y^2 - 21y + 7

What should you do after identifying the greatest common factor?

• Multiply it by each term

• Ignore it

• Add it to each term

• Factor it out from each term