Factoring Trinomials and GCF

The video tutorial explains how to factor algebraic expressions by first identifying and factoring out the greatest common factor. It provides two examples: one with the expression 5y^3 - 85y^2 + 360y and another with 6v^4 + 78v^3 + 216v^2. The tutorial emphasizes the importance of factoring completely and demonstrates how to break down trinomials into binomial factors, focusing on finding factors that add up to a specific sum.

What is the first step in any factoring problem?

• Combine like terms

• Expand the expression

• Identify the leading coefficient

• Factor out the greatest common factor

In the expression 5y^3 - 85y^2 + 360y, what is the greatest common factor?

• 5

• 85

• y

• 5y

After factoring out the GCF in the first expression, what is the resulting trinomial?

• y^2 - 17y - 72

• y^2 + 17y - 72

• y^2 - 17y + 72

• y^2 + 17y + 72

What are the factors of 72 that add up to -17?

• 6 and 12

• -6 and -12

• 8 and 9

• -8 and -9

What is the greatest common factor in the expression 6v^4 + 78v^3 + 216v^2?

• 6v

• 216v^2

• 78v

• 6v^2

After factoring out the GCF in the second expression, what is the resulting trinomial?

• v^2 - 13v - 36

• v^2 + 13v + 36

• v^2 + 13v - 36

• v^2 - 13v + 36

Which pair of numbers are factors of 36 that add up to 13?

• 4 and 9

• 6 and 6

• 2 and 18

• 3 and 12

What is the first step in factoring a trinomial with a leading coefficient of 1?

• Expand the trinomial

• Combine like terms

• Divide the trinomial by the leading coefficient

• Find two numbers that multiply to the constant term and add to the middle term

What is one of the binomial factors of the trinomial v^2 + 13v + 36?

• v + 6

• v - 4

• v - 6

• v + 4

What is the other binomial factor of the trinomial v^2 + 13v + 36?

• v + 9

• v + 12

• v - 9

• v - 12