Factoring Polynomials and GCF

The video tutorial explains how to factor a polynomial by identifying and using the greatest common monomial factor. It begins with finding the greatest common factor (GCF) of the coefficients, then moves on to factoring the variables. The tutorial demonstrates expressing each term as a product of the GCF and another monomial, and finally, it shows how to factor out the GCF from the entire expression. The process is verified by redistributing the GCF to ensure the original polynomial is obtained.

What is the first step in factoring a polynomial by its greatest common monomial factor?

• Identify the polynomial's degree.

• Find the greatest common factor of the coefficients.

• Simplify the polynomial.

• Determine the polynomial's roots.

What is the greatest common factor of the coefficients 8 and 12?

• 2

• 4

• 6

• 3

Which power of x is the greatest common factor for x^2 and x?

• x^2

• x

• 1

• x^3

What is the greatest common monomial factor of y and y^2?

• y^2

• 1

• y^3

• y

How can the term 8x^2y be expressed using the greatest common monomial factor 4xy?

• 4xy * 2y

• 4xy * x

• 4xy * 2x

• 4xy * 2

What is the product of 4xy and 3y?

• 12x^2y^2

• 12xy

• 12x^2y

• 12xy^2

What is the result of factoring out 4xy from the polynomial?

• 4xy(2 + 3)

• 4xy(2x + 3y)

• 4xy(x + y)

• 4xy(2x + y)

What operation is performed when factoring out the greatest common monomial factor?

• Subtraction

• Addition

• Division

• Multiplication

What is the purpose of factoring a polynomial by its greatest common monomial factor?

• To change the polynomial's coefficients.

• To find the roots of the polynomial.

• To simplify the polynomial.

• To increase the polynomial's degree.

What is the final expression after factoring the polynomial?

• 4xy(2 + 3)

• 2x + 3y

• 4xy(2x + 3y)

• 4xy + 2x + 3y