Factoring 4-Term Polynomials by Grouping

The video tutorial covers the method of factoring by grouping for four-term polynomials. It explains the process of grouping terms, factoring out the greatest common factor (GCF), and ensuring the binomials in parentheses are identical. The tutorial includes multiple examples, demonstrating how to factor polynomials completely, including handling differences of squares and polynomials with multiple variables. It emphasizes the importance of recognizing when a polynomial is not factorable.

When should you use the grouping method for factoring?

• When you have a polynomial with five terms

• When you have a polynomial with two terms

• When you have a polynomial with four terms

• When you have a polynomial with three terms

What is the first step in factoring by grouping?

• Factor out the GCF from the entire polynomial

• Combine like terms

• Group the first two terms and the last two terms

• Rewrite the polynomial in standard form

What should you do if the binomials in the parentheses are not the same after factoring out the GCF?

• Combine the terms again

• Factor out a different GCF

• Rewrite the polynomial in standard form

• The polynomial is not factorable

In the example where the polynomial is x^3 - 3x^2 + 4x - 12, what is the GCF of the first binomial?

• 4

• 3

• x^2

• x

What is the GCF of the second binomial in the example x^3 - 3x^2 + 4x - 12?

• x

• x^2

• 4

• 3

In the example x^3 - 3x^2 + 4x - 12, what should you factor out from the second binomial to make the parentheses match?

• x^2

• Negative 4

• x

• 4

What is the next step after grouping terms and factoring out the GCF in each binomial?

• Combine the GCFs

• Combine like terms

• Rewrite the polynomial in standard form

• Check for a difference of squares

In the example 5x^3 - 5x^2 - x + 3, what is the GCF of the first binomial?

• x^2

• 5x^2

• x

• 5x^3

What should you factor out from the second binomial in the example 5x^3 - 5x^2 - x + 3 to make the parentheses match?

• 5

• x

• Negative 1

• 1

What should you do if you cannot factor the polynomial to get the same terms in the parentheses?

• Combine like terms

• Rewrite the polynomial in standard form

• The polynomial is not factorable

• Factor out a different GCF