Factoring Expressions and GCF

The video tutorial explains how to factor algebraic expressions completely. It begins by identifying the greatest common factor among terms and demonstrates the process with two examples. The first example involves factoring an expression with positive terms, while the second example deals with negative terms. The tutorial emphasizes the importance of simplifying expressions by factoring out common factors and further breaking down the expression into simpler binomials.

What is the first step in factoring an expression completely?

• Identify the greatest common factor.

• Multiply all terms by 2.

• Add all terms together.

• Divide the expression by x.

Which number is the greatest common factor of 4, 8, and 12?

• 6

• 2

• 4

• 3

Which of the following is a common factor of all terms in the expression 4x² - 8x - 12?

• 5

• 4

• 3

• 2

After factoring out the greatest common factor, what is the next step?

• Find two numbers that add to a specific value and multiply to another.

• Divide the expression by x.

• Add the terms together.

• Multiply the terms by 2.

What is the purpose of finding two numbers that add to a specific value and multiply to another?

• To simplify the expression.

• To factor the expression further.

• To add more terms to the expression.

• To divide the expression by x.

What is the result of factoring 4x² - 8x - 12 completely?

• 4(x + 2)(x - 3)

• 4(x - 2)(x + 3)

• 4(x + 3)(x - 1)

• 4(x - 3)(x + 1)

What is the greatest common factor of -3x², 21x, and -30?

• 1

• 3

• -3

• 5

Why is it beneficial to factor out a negative number in some expressions?

• It adds more terms to the expression.

• It simplifies the expression by removing negative signs from the leading term.

• It makes the expression more complex.

• It makes the expression longer.

What is the result of factoring -3x² + 21x - 30 completely?

• 3(x - 5)(x - 2)

• -3(x + 5)(x + 2)

• 3(x + 5)(x + 2)

• -3(x - 5)(x - 2)

What is the benefit of factoring an expression completely?

• It makes the expression more complex.

• It adds more terms to the expression.

• It simplifies the expression for easier solving.

• It makes the expression longer.