Factoring Polynomials and GCF Concepts

This video tutorial covers the process of factoring polynomials using common monomial factors. It begins with an introduction to the concept, followed by detailed examples of factoring a binomial, a polynomial with two terms, and a trinomial with three terms. Each example demonstrates the step-by-step process of identifying the greatest common factor (GCF) and simplifying the expression. The video emphasizes the importance of checking work by redistributing the factored expression to ensure it matches the original polynomial.

What is the first step in factoring polynomials using common monomial factors?

• Finding the greatest common factor

• Adding all terms together

• Multiplying all terms by a constant

• Dividing each term by the highest exponent

What is the common factor in the binomial 3x^3 + 6x?

• 3

• 6x

• x

• 3x

How do you determine what goes inside the parentheses when factoring?

• By adding the terms

• By multiplying the terms

• By dividing each term by the common factor

• By subtracting the terms

What should you do to verify the factored form of a polynomial?

• Subtract the terms inside the parentheses

• Add the terms inside the parentheses

• Multiply the factored expression back out

• Divide the original polynomial by the factored form

What is the GCF of the constants 21 and 14?

• 21

• 3

• 7

• 14

When dividing terms by the GCF, what happens to the exponents?

• They remain unchanged

• They are multiplied

• They are added together

• They are subtracted

Why is it important to be careful with negative signs when factoring?

• They are only important in addition

• They make no difference

• They can change the entire expression

• They are always ignored

What is the GCF of the terms 4x^2y, 2xy^2, and 8x^2y^2?

• x^2y^2

• 8xy

• 2xy

• 4xy

What is the result of dividing 4x^2y by 2xy?

• 4xy

• x^2

• 2xy

• 2x

What is a good way to check if your factored expression is correct?

• Add all terms together

• Multiply the factored expression back out

• Divide the original polynomial by the factored form

• Subtract the terms inside the parentheses