Factoring and GCF Concepts

The video tutorial explains how to factor expressions completely by first identifying and factoring out the greatest common factor (GCF) before applying other methods like the difference of squares. It demonstrates this process with two examples: 16t^2 - 64 and y^4 - 25y^2. The tutorial also highlights common mistakes, such as applying the difference of squares without factoring out the GCF, and corrects them to show the importance of following the correct steps. The video concludes with a summary of the techniques discussed.

What is the first step in factoring any expression?

• Factor out the greatest common factor

• Apply the difference of squares formula

• Multiply the terms

• Identify perfect squares

What is the greatest common factor of 16t^2 and 64?

• 2

• 16

• 4

• 8

After factoring out the GCF from 16t^2 - 64, what expression is left?

• t^2 - 4

• 4t^2 - 16

• t^2 - 16

• 4t^2 - 4

What are the binomial factors of t^2 - 4?

• (t + 4)(t - 4)

• (t + 3)(t - 3)

• (t + 2)(t - 2)

• (t + 1)(t - 1)

Why is it incorrect to apply the difference of squares formula first without factoring out the GCF?

• It leads to incorrect factors

• It is a longer process

• It results in more complex expressions

• It is not mathematically valid

What is the GCF of y^4 and 25y^2?

• 5

• 25

• y^4

• y^2

After factoring out y^2 from y^4 - 25y^2, what expression remains?

• y^2 - 25

• y^2 - 10

• y^2 - 15

• y^2 - 5

What are the binomial factors of y^2 - 25?

• (y + 2)(y - 2)

• (y + 3)(y - 3)

• (y + 5)(y - 5)

• (y + 4)(y - 4)

What is the correct factored form of y^4 - 25y^2?

• y^2(y + 4)(y - 4)

• y^2(y + 2)(y - 2)

• y^2(y + 3)(y - 3)

• y^2(y + 5)(y - 5)

What is the benefit of factoring out the GCF first?

• It simplifies the expression

• It makes the expression more complex

• It is a faster method

• It is not necessary