Factoring Polynomials: Finding the GCF

In this video, Betsy explains how to factor polynomials by identifying and factoring out the greatest common factor. She provides four examples, each demonstrating different scenarios, such as dealing with multiple terms, variables, and negative leading coefficients. The video aims to help students understand the process of factoring polynomials step-by-step.

What is the greatest common factor of 12 and 15?

• 6

• 12

• 15

• 3

When factoring polynomials, if all terms contain the same variable, what should you do?

• Ignore the variable

• Factor out the variable with the highest exponent

• Factor out the variable and ignore the exponents

• Factor out the variable with the lowest exponent

If a term in the polynomial does not have an exponent shown, what is its exponent?

• 2

• 1

• 0

• It does not have an exponent

What is the greatest common factor of 20, 15, and 25?

• 5

• 25

• 15

• 20

When factoring polynomials, what do you do with the variable with the smallest exponent?

• Subtract it from the highest exponent

• Add it to the highest exponent

• Factor it out

• Ignore it

How many terms must the factored expression have if the original polynomial has three terms?

• It varies

• Three

• Two

• One

If a polynomial has terms with different variables, what should you consider when factoring?

• The variable present in all terms

• The variable with the highest exponent

• Only the numerical coefficients

• Each variable and its smallest exponent

In the process of factoring, if you factor out a '3' from the terms 21, 27, and 18, what is the next step?

• Add 3 to each term

• Divide each term by 3

• Subtract 3 from each term

• Multiply each term by 3

What is the first step in factoring polynomials with a negative leading coefficient?

• Ignore the negative sign

• Divide all terms by the leading coefficient

• Factor out the negative sign

• Multiply all terms by -1

What is the result of factoring out the greatest common factor from the polynomial -3m^2 + 12m - 6?

• -3(m^2 - 4m + 2)

• 3(m^2 - 4m + 2)

• 3(m^2 + 4m - 2)

• -3(m^2 + 4m - 2)