Factoring Expressions and GCF

The video tutorial explains how to factor algebraic expressions completely by first identifying the greatest common factor (GCF) and then further factoring using techniques like the difference of squares and trinomial factoring. Two examples are provided: the first involves factoring 2x^3 - 50x by identifying the GCF as 2x and then recognizing a difference of squares. The second example factors 3x^3 + 9x^2 - 84x by finding the GCF of 3x and then factoring the resulting trinomial. The tutorial emphasizes the importance of starting with the GCF and provides a clear, step-by-step approach to factoring.

What is the first step in factoring any expression?

• Factor into binomials

• Check for a difference of cubes

• Identify the greatest common factor

• Look for a difference of squares

What is the greatest common factor of 2x^3 and 50x?

• 50

• 2

• x

• 2x

After factoring out the GCF from 2x^3 - 50x, what type of expression is left?

• Sum of cubes

• Difference of squares

• Monomial

• Trinomial

What is the GCF of the terms in the expression 3x^3 + 9x^2 - 84x?

• 9

• 3x

• x

• 3

What is the expression inside the parentheses after factoring out the GCF from 3x^3 + 9x^2 - 84x?

• x^2 + 3x - 28

• x^2 - 3x + 28

• x^2 - 9x + 84

• x^2 + 9x - 84

Which pair of numbers multiplies to -28 and adds to 3?

• -4 and 7

• -7 and 4

• 4 and -7

• 7 and -4

What are the binomial factors of x^2 + 3x - 28?

• (x - 4)(x + 7)

• (x - 4)(x - 7)

• (x + 4)(x + 7)

• (x + 4)(x - 7)

What is the complete factorization of 3x^3 + 9x^2 - 84x?

• 3x(x - 4)(x + 7)

• 3x(x + 4)(x - 7)

• 3x(x + 4)(x + 7)

• 3x(x - 4)(x - 7)

Why is it important to factor out the greatest common factor first?

• It simplifies the expression for further factoring

• It makes the expression a monomial

• It changes the expression into a sum of cubes

• It eliminates the need for further factoring

What is the significance of the order of binomial factors in the final expression?

• The order determines the type of expression

• The order does not matter

• The order affects the GCF

• The order changes the value of the expression