Factoring Polynomials and GCF

The video tutorial covers factoring polynomials, focusing on two methods: using the greatest common factor (GCF) and factoring by grouping. It begins with an introduction to the concept of factoring, followed by a detailed explanation of how to identify and extract the GCF from polynomial terms. The tutorial then transitions to factoring by grouping, demonstrating how to rearrange and group terms to simplify the polynomial. Each method is illustrated with examples, providing a step-by-step guide to understanding and applying these techniques.

What is the main focus of this video tutorial?

• Solving quadratic equations

• Factoring polynomials

• Solving inequalities

• Graphing linear equations

What is the greatest common factor?

• The smallest number that divides all terms

• The product of all variables

• The largest number that divides all terms

• The sum of all coefficients

In the trinomial 6x^2y^2 - 22xy^2 + 6x^3y, what is the greatest common factor of the coefficients?

• 6

• 2

• 3

• 1

What is the greatest common factor of the x terms in the trinomial?

• x^2

• x^3

• x

• 1

What is the greatest common factor of the y terms in the trinomial?

• y

• y^2

• y^3

• 1

What is the greatest common factor of the y terms in the trinomial?

• y^3

• 1

• y

• y^2

After factoring out the greatest common factor, what is the expression inside the parentheses for the trinomial?

• 2xy^2 - y^2 + 2x^2y

• 3x^2y^2 - xy^2 + 3x^3y

• x^2y^2 - xy^2 + x^3y

• 3xy^2 - y^2 + 3x^2y

What is the result of factoring 6x^2y^2 - 22xy^2 + 6x^3y completely?

• 2xy^2(3x - 1 + 3x^2)

• 2x(3xy^2 - y^2 + 3x^2y)

• 2xy(3xy - y + 3x^2)

• 2x^2y(3y - 1 + 3x)

What is the result of factoring 6x^2y^2 - 22xy^2 + 6x^3y completely?

• 2xy(3xy - y + 3x^2)

• 2x(3xy^2 - y^2 + 3x^2y)

• 2xy^2(3x - 1 + 3x^2)

• 2x^2y(3y - 1 + 3x)

What is the result of factoring 6x^2y^2 - 22xy^2 + 6x^3y completely?

• 2xy(3xy - y + 3x^2)

• 2x(3xy^2 - y^2 + 3x^2y)

• 2x^2y(3y - 1 + 3x)

• 2xy^2(3x - 1 + 3x^2)