Factoring Polynomials and Expressions

This video tutorial covers the basics of factoring expressions and solving quadratic equations by factoring. It begins with simple expressions, demonstrating how to factor using the greatest common factor (GCF). The tutorial progresses to more complex expressions involving multiple variables and introduces the difference of squares method. It also covers solving quadratic equations by factoring, providing step-by-step examples. Advanced techniques for factoring complex trinomials are also discussed, ensuring a comprehensive understanding of the topic.

What is the greatest common factor (GCF) of the expression 3x + 6?

• 1

• 2

• 3

• 6

How would you factor the expression 9a^2b^3 + 12a^3b^4?

• 3a^2b^3(3 + 4a^3b)

• 3a^2b^3(3 + 4ab^2)

• 3a^2b^3(3 + 4a^2b)

• 3a^2b^3(3 + 4ab)

Which of the following is a correct factorization of x^2 - 16?

• (x - 3)(x + 5)

• (x - 2)(x + 8)

• (x - 4)(x + 4)

• (x - 8)(x + 2)

What is the factored form of 64 - x^2?

• (8 - x)(8 + x)

• (x - 8)(x + 8)

• (x - 8)(x - 8)

• (8 - x)(8 - x)

To solve the quadratic equation x^2 + 4x = 21 by factoring, what should be the first step?

• Divide both sides by x

• Multiply both sides by 2

• Subtract 21 from both sides

• Add 21 to both sides

Which pair of numbers can be used to factor the quadratic equation x^2 - 9x + 20?

• -3 and -7

• 3 and 7

• -4 and -5

• 4 and 5

When factoring 3x^2 - 72 = 15x, what is the GCF that can be factored out first?

• 1

• 15

• 3

• 5

In the expression 6x^2 + x - 12, what is the product of the leading coefficient and the constant term?

• -72

• 72

• 12

• -12

What is the correct factorization of 15x^2 + 23x - 28?

• (3x - 4)(5x + 7)

• (3x + 4)(5x - 7)

• (5x - 4)(3x + 7)

• (5x + 4)(3x - 7)

Which method is used to factor a trinomial with four terms?

• Difference of squares

• Grouping

• Quadratic formula

• Completing the square