Factoring by GCF: Key Concepts and Techniques

What is the first step in factoring polynomials discussed in the video?

• Finding the greatest common factor

• Identifying the highest exponent

• Applying the distributive property

• Using the zero product property

What property is used to simplify the expression 2x(x - 7)?

• Identity property

• Commutative property

• Distributive property

• Associative property

How is the GCF used in the process of factoring polynomials?

• It is subtracted from each term

• It is multiplied with each term

• It is divided out from each term

• It is added to each term

In the context of the video, what does factoring by GCF reverse?

• The distributive property

• The commutative property

• The zero product property

• The associative property

When factoring by GCF, what determines the greatest common factor in terms of variables?

• The variable with the lowest exponent

• The variable with the highest coefficient

• The variable with the highest exponent

• The variable with the lowest coefficient

What is the result of factoring the polynomial 4x^4 + 24x^3 by its GCF?

• 4x(x^3 + 6x^2)

• 4(x^3 + 6x^2)

• 4x^3(x^4 + 6x^3)

• 4x^3(x + 6)

What must be true for the zero product property to be applied?

• The equation must be set to zero

• The equation must be set to one

• The equation must include addition

• The equation must include subtraction

What does the zero product property state about a product equal to zero?

• At least one of the factors must be zero

• All factors must be zero

• The factors must be prime numbers

• The factors must include a variable

What is the significance of setting an equation to zero in solving polynomial equations?

• It eliminates all variables from the equation

• It helps in identifying the GCF

• It simplifies the equation to its basic form

• It allows the use of the zero product property

What time does the ball return to zero height after being kicked, according to the problem solved?

• 10 seconds

• 7 seconds

• 3 seconds

• 5 seconds