Factoring Expressions and GCF

This video tutorial covers the process of factoring polynomials using the greatest common factor (GCF) and the difference of two perfect squares. It provides multiple examples, including how to use a graphing calculator to find the GCF. The tutorial also explores different approaches to factoring and highlights common mistakes. By the end, viewers will understand how to factor polynomials completely using these methods.

What are the two methods of factoring discussed in the introduction?

• Sum of cubes and difference of cubes

• Difference of two perfect squares and sum of squares

• Greatest common factor and difference of two perfect squares

• Greatest common factor and sum of cubes

What is the first step in factoring a polynomial completely?

• Check for a sum of squares

• Find the greatest common factor

• Use a graphing calculator

• Look for a difference of cubes

What is the result of factoring a difference of two perfect squares?

• A sum of squares

• A product of two binomials

• A single monomial

• A sum of cubes

What is the purpose of factoring polynomials?

• To solve equations

• To simplify expressions

• All of the above

• To find roots

In the first example, what is the greatest common factor of 2x^2 - 50?

• 10

• 5

• 25

• 2

After factoring out the greatest common factor in the first example, what expression is left inside the parentheses?

• x^2 - 50

• x^2 - 25

• 2x^2 - 25

• x^2 + 25

What is the final factored form of 2x^2 - 50?

• 2(x + 5)(x - 5)

• 2(x + 25)(x - 25)

• 2(x^2 - 25)

• 2(x^2 + 25)

In the second example, what is the greatest common factor of 3a^2 - 27?

• 3

• 9

• 27

• 1

What is the expression inside the parentheses after factoring out the greatest common factor in the second example?

• 3a^2 - 9

• a^2 - 9

• a^2 - 27

• a^2 + 9

What is the final factored form of 3a^2 - 27?

• 3(a + 3)(a - 3)

• 3(a^2 + 9)

• 3(a^2 - 9)

• 3(a + 9)(a - 9)