Factoring Polynomials and GCF Concepts

The video tutorial introduces factoring polynomials, emphasizing the importance of identifying and factoring out the greatest common factor (GCF). It explains the difference between polynomial and factored forms, using examples to demonstrate the process of factoring binomials and trinomials. The tutorial also covers handling negative signs in factoring and concludes with homework instructions.

What is the first step in factoring polynomials?

• Simplifying the expression

• Factoring out the greatest common factor

• Multiplying the terms

• Finding the roots

What does converting a polynomial form to a factored form involve?

• Changing addition to subtraction

• Changing multiplication to division

• Changing addition to multiplication

• Changing division to addition

In the example of factoring 5x^3 + 10x, what is the greatest common factor?

• 5x^2

• 10x

• 5x

• x^2

When factoring a binomial, what remains after factoring out the GCF?

• A monomial

• A binomial

• A trinomial

• A single term

What should you do to verify your factoring work?

• Divide the terms

• Subtract the terms

• Multiply the terms back together

• Add the terms back together

In the example with more variable factors, what is the GCF of 4a^2b^3 and 8ab^2?

• 8a^2b^3

• 4ab^2

• 8ab

• 4a^2b

How does factoring a trinomial differ from factoring a binomial?

• It requires a different GCF

• It involves more terms left behind

• It results in a single term

• It uses a different method

What is the GCF in the example with negative signs: -16x^2 + 48x?

• -16x^2

• 16x

• -16x

• 48x

What is left behind when the GCF is one of the terms?

• A factor of one

• The GCF itself

• Zero

• A new term

Why is it important to consider negative signs when factoring?

• They are ignored in factoring

• They simplify the process

• They affect the sign of the terms left behind

• They change the GCF