The video tutorial explains how to factor a given expression to identify removable and non-removable discontinuities. It begins with an introduction to the problem, emphasizing the need for factoring. The instructor demonstrates factoring the numerator and denominator, identifying the difference of squares and the factors of the denominator. The tutorial then focuses on identifying discontinuities, explaining the concept of removable and non-removable discontinuities, and concludes with a brief mention of further examples.

What is the first step in identifying discontinuities in a rational function?

• Graph the function

• Convert to decimal form

• Factor the expression

• Differentiate the function

Which of the following represents a difference of squares?

• X^2 + 5X + 6

• X^2 - 9

• X^2 - 5X + 6

• X^2 + 9

What are the factors of the expression X^2 + 5X + 6?

• X - 1 and X - 6

• X + 2 and X + 3

• X - 2 and X - 3

• X + 1 and X + 6

What type of discontinuity is present at X = -3 in the given function?

• Infinite discontinuity

• Jump discontinuity

• Non-removable discontinuity (asymptote)

• Removable discontinuity (hole)

Which value of X represents a non-removable discontinuity in the function?

• X = -3

• X = 0

• X = 2

• X = -2