Factoring by Grouping Techniques

What is the essential question discussed in the introduction?

• How to recognize different types of polynomials?

• How to factor trinomials?

• What is the greatest common factor?

• Is it possible to factor a four-term polynomial with no GCF?

What is the first step in factoring a four-term polynomial by grouping?

• Combine like terms

• Factor out the GCF from the entire polynomial

• Group the first two terms and the last two terms

• Check for a difference of perfect squares

When factoring by grouping, what should you do if the GCF of the second group is positive?

• Multiply the GCF by -1

• Ignore the GCF

• Add a plus sign before the GCF

• Subtract the GCF

In the example with x^3 + 7x^2 + 2x + 14, what is the GCF of the first group?

• 2

• 7

• x^2

• x

What should you do if the leading coefficient of the second group is negative?

• Combine the terms as they are

• Add a positive sign

• Ignore the negative sign

• Factor out a negative GCF

What indicates that a polynomial might be a difference of perfect squares?

• It has four terms

• It has a quadratic term with a minus sign in between

• It has a positive leading coefficient

• It has no GCF

In the example 54R^3 + 9R^2 - 24R - 4, what is the GCF of the first group?

• 54

• 9R^2

• R^2

• R

What is the final step in factoring by grouping if you identify a difference of perfect squares?

• Combine like terms

• Factor out the GCF

• Factor the difference of squares

• Group the terms again

In the example with 9N^2 - 7N - 1, what is the GCF of the second group?

• 9

• N

• -1

• 1

What should you do if the terms inside the parentheses are not the same after grouping?

• Add a plus sign

• Check for a mistake or determine if the polynomial is prime

• Factor out a different GCF

• Combine the terms as they are