Prime Factorization and Simplification

The video tutorial explains prime factorization using a factor tree method. It demonstrates the process with two examples: factorizing the number 75 and the number 54, both involving variables and exponents. The tutorial highlights how to break down numbers into their prime factors and express them in exponential form.

What is the purpose of prime factorization?

• To identify all prime numbers that multiply to form the original number

• To find the sum of all numbers

• To divide numbers into equal parts

• To convert numbers into fractions

Which of the following is a prime number?

• 3

• 4

• 6

• 9

How can the number 75 be expressed using its prime factors?

• 2 * 5 * 7

• 3 * 5 * 5

• 5 * 5 * 5

• 3 * 3 * 3

What is the correct expression for m cubed?

• m * m * m

• 3m

• m + m + m

• m^2

What is the first step in the prime factorization of 54?

• Divide by 5

• Divide by 2

• Divide by 3

• Divide by 7

How can the expression 2 * 3 * 3 * 3 * x * x be simplified?

• 2 * 3^3 * x

• 2 * 3 * x^3

• 2 * 3^2 * x^3

• 2 * 3^3 * x^2