Learn how to find the holes of a rational function removable discontinuities

The video tutorial explains the concept of discontinuity at X=5, emphasizing that X cannot equal 5. The teacher guides through the factoring process, focusing on finding two numbers that multiply to -10 and add to -3. The expression X-5 * X+2 is simplified, and the discontinuity is identified as a removable hole. The session concludes with a task for students to apply the learned concepts.

What is the value of x where the discontinuity occurs?

• x = 10

• x = -5

• x = 5

• x = 3

Which two numbers multiply to -10 and add to -3?

• -10 and 1

• 10 and -1

• -5 and 2

• 5 and -2

What is the factored form of the expression before division?

• (x - 2)(x + 5)

• (x + 2)(x - 5)

• (x - 5)(x + 2)

• (x + 5)(x - 2)

What happens to the discontinuity at x = 5 after factoring?

• It becomes a vertical asymptote

• It remains a discontinuity

• It becomes a removable hole

• It disappears completely

Why is the discontinuity at x = 5 considered removable?

• Because it can be canceled out

• Because it is a jump discontinuity

• Because it is a vertical asymptote

• Because it is an endpoint