Factoring Polynomials and GCF

The video tutorial explains the process of factoring expressions by first identifying and factoring out the greatest common factor. It provides two examples: factoring 4x^2 + 20x - 24 and 8w^2 - 32w - 96. The tutorial emphasizes the importance of simplifying expressions by factoring out the greatest common factor and then breaking down trinomials into binomial factors. The process involves identifying factors of the constant term that add up to the middle term's coefficient.

What is the first step in any factoring problem?

• Identify the leading coefficient

• Factor out the greatest common factor

• Simplify the expression

• List all possible factors

What is the greatest common factor of the expression 4x^2 + 20x - 24?

• 6

• 8

• 4

• 2

After factoring out the GCF from 4x^2 + 20x - 24, what expression is left inside the parentheses?

• x^2 + 4x - 6

• x^2 + 5x - 6

• x^2 + 6x - 5

• x^2 + 5x - 4

Which pair of numbers are the correct factors of -6 that add up to 5?

• -1 and 6

• -6 and 1

• -3 and 2

• -2 and 3

What is the greatest common factor of the expression 8w^2 - 32w - 96?

• 8

• 4

• 12

• 16

After factoring out the GCF from 8w^2 - 32w - 96, what expression is left inside the parentheses?

• w^2 - 4w - 16

• w^2 - 8w - 16

• w^2 - 4w - 12

• w^2 - 8w - 12

Which pair of numbers are the correct factors of -12 that add up to -4?

• -6 and 2

• -4 and 3

• -3 and 4

• -2 and 6

What is one of the binomial factors of the trinomial w^2 - 4w - 12?

• w + 2

• w - 2

• w - 6

• w + 6

What is the other binomial factor of the trinomial w^2 - 4w - 12?

• w + 2

• w - 6

• w - 2

• w + 6

What is the importance of factoring out the greatest common factor first?

• It increases the complexity of the expression

• It eliminates the need for further factoring

• It changes the expression completely

• It simplifies the expression for easier factoring