Factoring and Prime Factorization Concepts

The video tutorial explains how to find the least common denominator (LCD) for rational expressions. It begins with an introduction to the concept and outlines the steps to factor denominators and identify the LCD. Several examples are provided, demonstrating how to handle different types of denominators, including complex, factored, and opposite denominators. The tutorial emphasizes the importance of identifying the greatest occurrence of each factor to determine the LCD.

What is the first step in finding the least common denominator (LCD) of rational expressions?

• Subtract all denominators

• Add all denominators

• Factor all denominators

• Multiply all denominators

When finding the LCD, what should you do after factoring the denominators?

• Ignore the factors

• Add the factors

• Subtract the factors

• Circle the greatest occurrence of each factor

In the first example, what is the prime factorization of 6?

• 2 * 2

• 3 * 3

• 2 * 3

• 5 * 1

For the first example, which factor occurs the most in the denominators?

• x

• y

• 3

• 2

In the second example, what is the prime factorization of 14?

• 3 * 5

• 2 * 7

• 2 * 5

• 3 * 7

For the second example, which variable has the greatest occurrence?

• m

• n

• x

• y

In the third example, which factor is different between the two binomials?

• m - 1

• m + 2

• m + 1

• m - 2

For the third example, how many times does the factor m + 2 occur in the first denominator?

• Four times

• Twice

• Once

• Three times

In the fourth example, what type of expression is x^2 - 4?

• Trinomial

• Binomial

• Sum of squares

• Difference of squares

For the fourth example, which factor occurs in both denominators?

• x + 2

• x - 2

• x + 1

• x - 1