Factoring and Distributing Expressions

This lesson teaches how to factor quadratic expressions by identifying and using the greatest common factor (GCF). It begins with an introduction to factors, using numbers like 12, 18, and 27 to illustrate the concept. The lesson then explains how to find common factors and apply this knowledge to factor quadratic expressions, such as 18x^2 - 27x. The process involves listing factors, identifying the GCF, and simplifying the expression. The lesson concludes with a verification step to ensure the factoring is correct.

What are the factors of the number 12?

• 3 and 5

• 2 and 6

• 4 and 3

• 1 and 11

Which of the following is a factor of x squared?

• x and x

• x and 3

• x and 2

• x and 1

What is the greatest common factor of 18 and 27?

• 3

• 6

• 12

• 9

What is the greatest common factor of the terms in the expression 18x^2 - 27x?

• 6x

• 9x

• 3x

• 12x

After factoring out the greatest common factor from 18x^2 - 27x, what is the remaining expression?

• 2x + 3

• 3x - 2

• 2x - 3

• 3x + 2

What is the result of distributing 9x times 2x?

• 27x

• 18x^2

• 27x^2

• 18x

What is the result of distributing 9x times 3?

• 27x^2

• 27x

• 18x^2

• 18x

Why is it important to verify the factored form by distributing?

• To ensure the expression is simplified

• To check if the original expression is obtained

• To find new factors

• To change the expression

What method is used in this lesson to factor a quadratic expression?

• Completing the square

• Quadratic formula

• Greatest common factor

• Synthetic division

What is the final factored form of 18x^2 - 27x?

• 9x(3x + 2)

• 9x(3x - 2)

• 9x(2x - 3)

• 9x(2x + 3)