Factoring Differences of Squares and Solving Polynomial Equations

This video tutorial covers the concept of factoring differences of squares, a special case in polynomial factoring. It explains the pattern used to factor expressions like a^2 - b^2 into (a + b)(a - b). The tutorial provides examples of basic factoring and introduces the concept of factoring with the greatest common factor (GCF). It also demonstrates solving polynomial equations by setting them to zero, factoring, and solving for the variable. The video emphasizes the importance of recognizing perfect squares and using the commutative property of multiplication.

What is the result of factoring the expression a² - b²?

• a² + b²

• a + b

• a - b

• (a + b)(a - b)

Which of the following is a perfect square?

• 90

• 75

• 64

• 50

What is the factored form of K² - 100?

• (K + 20)(K - 20)

• (K + 5)(K - 5)

• (K + 1)(K - 1)

• (K + 10)(K - 10)

What is the factored form of 4y² - 121?

• (2y + 11)(2y - 11)

• (4y + 121)(4y - 121)

• (4y + 11)(4y - 11)

• (2y + 121)(2y - 121)

What should you do first when factoring 8y² - 32?

• Multiply the terms

• Check for a perfect square

• Add the terms

• Factor out the GCF

What is the GCF of 50 and 18?

• 2

• 5

• 10

• 25

What is the factored form of 2x² - 128y²?

• 2(x + 32y)(x - 32y)

• 2(x + 16y)(x - 16y)

• 2(x + 64y)(x - 64y)

• 2(x + 8y)(x - 8y)

What is the GCF of 36y³ - 9y?

• 3y

• 9y

• 18y

• 12y

What is the first step in solving the equation 4x² - 25 = 0?

• Set the equation equal to zero

• Factor the equation

• Subtract 25 from both sides

• Add 25 to both sides

What are the solutions to the equation 16y² - 81 = 0?

• y = ±9/4

• y = ±16/81

• y = ±81/16

• y = ±4/9