Factoring Polynomials and GCF

The video tutorial explains how to factor expressions completely by first identifying the greatest common factor and then factoring trinomials into binomials. It covers two examples: 4x^2 - 10x - 6 and 18x^3 - 33x^2 + 12x, using methods like trial and error to find the correct binomial factors. The tutorial emphasizes the importance of including the greatest common factor in each step and checking the work to ensure accuracy.

What is the first step in any factoring problem?

• Find the roots of the equation

• Identify the leading coefficient

• Simplify the expression

• Factor out the greatest common factor

What is the greatest common factor of the expression 4x^2 - 10x - 6?

• 6

• 2

• 10

• 4

When factoring the trinomial 2x^2 - 5x - 3, what method is used?

• Bottoms up

• Trial and error

• Grouping

• Synthetic division

What is the correct factored form of 2x^2 - 5x - 3?

• 2(x - 3)(x + 1)

• 2(x + 3)(x - 1)

• 2(2x + 1)(x - 3)

• 2(x + 1)(2x - 3)

Tags

CCSS.6.EE.A.3

What property allows the order of binomials to be changed in multiplication?

• Associative property

• Identity property

• Distributive property

• Commutative property

What is the greatest common factor of the expression 18x^3 - 33x^2 + 12x?

• 9x

• 6x

• 3x

• 12x

In the second example, what are the factors of the trinomial 6x^2 - 11x + 4?

• (3x - 4)(2x - 1)

• (2x - 2)(3x - 1)

• (6x - 1)(x - 4)

• (3x - 2)(2x - 2)

Why can't there be a common factor in either binomial after factoring out the GCF?

• It would simplify the expression further

• It would make the expression incorrect

• It would mean the GCF was not factored out completely

• It would change the leading coefficient

What is the final factored form of 18x^3 - 33x^2 + 12x?

• 3x(6x - 1)(x - 4)

• 3x(2x - 2)(3x - 1)

• 3x(3x - 4)(2x - 1)

• 3x(2x - 4)(3x - 1)

What is the purpose of verifying the factored form?

• To identify any remaining common factors

• To check if the original expression is obtained

• To ensure the expression is simplified

• To find the roots of the expression