Limit and Factor Techniques in Algebra

This video tutorial explains how to solve limits by factoring. It covers several examples, demonstrating the process of factoring polynomials to resolve indeterminate forms and find limits. The video emphasizes the importance of direct substitution before manipulation and highlights cases where limits are undefined due to vertical asymptotes.

What is the first step in solving a limit problem?

• Graph the function

• Factor the expression

• Directly substitute the approaching value

• Use L'Hôpital's Rule

In the expression x^2 + x - 20, which two numbers multiply to -20 and add to 1?

• 10 and -2

• 4 and -5

• 5 and -4

• 2 and -10

What is the result of canceling out the common factor in the expression (x^2 + x - 20)/(x - 4) after factoring?

• x + 5

• x - 5

• x - 4

• x + 4

What is the limit as X approaches 4 of (x^2 + x - 20)/(x - 4)?

• 4

• 5

• 9

• 0

How do you factor x^2 - 64?

• (x - 16)(x + 16)

• (x - 4)(x + 4)

• (x - 32)(x + 32)

• (x - 8)(x + 8)

What is the limit as X approaches 8 of (x^2 - 64)/(x - 8)?

• 64

• 0

• 16

• 8

What is the first step in solving the limit as X approaches 1 of (6x^3 - 6x^2)/(x^4 - x^2)?

• Use the quadratic formula

• Apply L'Hôpital's Rule

• Graph the function

• Factor out 6x^2 from the numerator

What is the limit as X approaches 1 of (6x^3 - 6x^2)/(x^4 - x^2) after simplification?

• 1

• 2

• 3

• 4

Why is the limit as X approaches 2 of (x^2 - 2x + 2)/(x - 2) undefined?

• Both numerator and denominator are zero

• The numerator is zero

• The denominator is zero

• The function is continuous

What should you always try first when solving limits?

• Graph the function

• Direct substitution

• Use L'Hôpital's Rule

• Factor the expression