Factoring Polynomials by Grouping Techniques

This video tutorial covers the method of factoring by grouping, focusing on problems with four terms. It provides step-by-step examples, starting with basic problems and progressing to more challenging ones. The tutorial also introduces the concept of the difference of squares, demonstrating how to factor expressions further. Key techniques include identifying common factors, grouping terms, and applying the difference of squares formula.

What is required for the process of factoring by grouping?

• Exactly four terms

• Prime numbers only

• At least two terms

• Any number of terms

What do you obtain when you factor out x squared from the first group in the first example?

• X plus 3

• X squared plus 3

• X minus 3

• 3X squared

What common factor is identified in the second group of the first example?

• X squared

• 21

• X plus 3

• 7

After factoring by grouping in the first example, what expression is factored out from both groups?

• X plus 3

• X squared

• 3X squared

• 7

In the second example, what is the greatest common factor between the terms 9X to the third and -12X squared?

• 3X

• 3X squared

• 9

• 12

What is factored out from the second group in the second example?

• 3X minus 4

• -1

• 3X

• X squared

What common factor is extracted from the first group in the challenging problem?

• 9

• X squared

• -9

• 2X plus 5

What additional factorization is performed on the expression X squared minus 9 in the challenging problem?

• X plus 3 times X minus 3

• X minus 3

• X squared plus 9

• 2X plus 5

What does the expression X squared minus 9 represent in terms of algebraic structures?

• Sum of squares

• Difference of squares

• Perfect square trinomial

• Quadratic equation

What is the final factored form of the challenging problem?

• (X squared minus 9)

• (2X plus 5)(X squared minus 9)

• (X plus 3)(X minus 3)

• (2X plus 5)(X plus 3)(X minus 3)