Factoring Numerical and Algebraic Expressions

In this video, Jeff Jacobs introduces the concept of factoring expressions, focusing on using the greatest common factor (GCF). The tutorial begins with a simple numerical example, factoring 20-12, and progresses to more complex algebraic expressions. Each example demonstrates the process of identifying the GCF and factoring it out, akin to reversing the distributive property. The video concludes with a challenging example involving variables and a brief practice session.

What is the Greatest Common Factor (GCF) of 20 and 12?

• 4

• 2

• 6

• 3

How do you describe the process of factoring out the GCF from an expression?

• Subtracting the GCF from each term

• Multiplying each term by the GCF

• Dividing each term by the GCF

• Adding the GCF to each term

What is the first step in factoring expressions using the GCF?

• Divide each term by the GCF

• Identify the GCF

• Multiply each term by the GCF

• Write the expression in expanded form

How is factoring related to the distributive property?

• It's the process of adding a common factor

• It's unrelated to the distributive property

• It's the reverse process of distributing a common factor

• It involves multiplying the GCF by each term

What is the GCF of 36 and 9?

• 6

• 18

• 9

• 3

In the expression 28x + 21y, what is the GCF of the numerical coefficients?

• 28

• 21

• 14

• 7

What does factoring out the GCF from an algebraic expression involve?

• Combining like terms

• Solving for the variable

• Dividing each term by the GCF and writing what's left

• Multiplying each term by the GCF

When factoring an expression like 3x^2 + 12x, what common factors are considered?

• 3 and x

• 3 and x^2

• 12 and x

• 12 and x^2

After factoring out the GCF in the expression 3x^2 + 12x, what is left inside the parentheses?

• x + 4

• x^2 + 4

• 3x + 4

• x^2 + 12

Why is it important to factor expressions in mathematics?

• To multiply expressions more efficiently

• To add expressions without common factors

• To simplify expressions for easier manipulation

• To find the value of variables