Finding the Greatest Common Factor

This video tutorial explores factoring out the greatest common factor (GCF) using the area model. It begins with basic concepts of finding the area of a rectangle and understanding factors. The tutorial then introduces the GCF, explaining how to identify and use it to factor expressions. The box method is demonstrated as a tool for organizing and solving factoring problems. Advanced examples are provided to illustrate the application of these concepts, ensuring a comprehensive understanding of factoring using the GCF and area model.

What is the formula for finding the area of a rectangle?

• Length / Width

• Length - Width

• Length x Width

• Length + Width

If the area of a rectangle is 32, which of the following could be its side lengths?

• 4 and 8

• 3 and 9

• 5 and 6

• 2 and 16

What are factors in the context of multiplication?

• Numbers that subtract to a value

• Numbers that add up to a value

• Numbers that multiply to give a value

• Numbers that divide a value

Which of the following is a possible pair of factors for 15?

• 6 and 3

• 2 and 8

• 3 and 5

• 4 and 4

What is the greatest common factor (GCF)?

• The average of all factors

• The largest factor shared by all terms

• The smallest factor shared by all terms

• The sum of all factors

For the expression 2x^3 - 8x^2, what is the GCF?

• 4x^2

• 2x

• x

• 2x^2

How do you determine the GCF of two terms?

• By subtracting the coefficients

• By adding the coefficients

• By finding the largest common factor of the coefficients and variables

• By dividing the coefficients

What is the GCF of 15x^2 + 10?

• 10

• 3

• 5

• 15

In the expression 15x^2 + 10, what is the factored form using the GCF?

• 10(1.5x^2 + 1)

• 15(x^2 + 0.67)

• 5(3x^2 + 2)

• 3(5x^2 + 2)

What is the purpose of the box method in factoring?

• To add terms together

• To organize and visualize the factoring process

• To divide terms

• To subtract terms