Factoring and Prime Factorization Concepts

This video delves into the concept of factoring, starting with basic number factorization and moving into algebraic expressions. It covers the prime factorization of numbers and extends these ideas to algebra, demonstrating how to factor expressions like x squared plus 6x. The video then explores more advanced techniques for factoring higher order expressions, such as monomials and polynomials, emphasizing the importance of understanding these concepts for future algebraic problem-solving.

What is one way to factor the number 12?

• 6 times 5

• 3 times 4

• 2 times 5

• 4 times 5

What is the prime factorization of 12?

• 3 times 3 times 2

• 2 times 2 times 3

• 2 times 2 times 2

• 2 times 3 times 3

How can x squared plus 6x be factored?

• x times (6 + x)

• x times (x + 6)

• x times (x - 6)

• x times (6 - x)

What does factoring an expression involve?

• Adding expressions together

• Subtracting expressions from each other

• Writing an expression as a product of other expressions

• Writing an expression as a sum of other expressions

What is a monomial?

• A polynomial with three terms

• A single term expression

• A polynomial with four terms

• A polynomial with two terms

How can 6x to the seventh be factored?

• 2x to the third times 3x to the fourth

• 2x to the fourth times 3x to the third

• 3x to the third times 2x to the fourth

• 3x to the fourth times 2x to the third

What is another way to factor 6x to the seventh?

• x to the seventh times 6x

• x to the fifth times 6x

• x to the sixth times 6x

• x to the fourth times 6x

What is the prime factorization of 6?

• 3 times 3

• 3 times 4

• 2 times 2

• 2 times 3

How many x's are multiplied together in x to the seventh?

• 7

• 8

• 6

• 5

Why is understanding monomials important?

• For dividing polynomials

• For adding polynomials

• For subtracting polynomials

• For factoring higher degree polynomials