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## Integrated math 3

### Course: Integrated math 3>Unit 2

Lesson 1: Factoring monomials

# Which monomial factorization is correct?

Factoring monomials involves breaking down an expression into two parts. This process shows that there are multiple correct ways to factor a monomial. By multiplying coefficients and powers, you can verify if the factorization is accurate. It's a fun exploration of the many ways to dissect monomials!

## Want to join the conversation?

• What's FOIL? Does it work here?
• A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial. Then simplify the products and combine any like terms which may occur.
• will the product of two monomials always be a monomial, on the same note will the product of two polynomials always be a polynomial?
• yes a monomial times a monomial will be a monomial and a polynomial times a polynomial is a polynomial
• i have no idea what im doing right now
• i dont understand any of this.
• what is monomial
(1 vote)
• A monomial is an algebraic expression with only one term. For instance, "2x" is a monomial. So is "3xy."

If the expression has 2 terms (like, 2x + 3y), it's a binomial; if it has 3 terms (like, ax + by + c), it's a trinomial, etc.

Hope this helps!
• Will the product of two monomials always be a monomial, on the same note will the product of two polynomials always be a polynomial?
(1 vote)
• Both of those things are true. Also understand that a monomial is a type of polynomial, so the product of a monomial with a polynomial will be a polynomial, but may or may not be a monomial.
• there are many ways yes but is there a best way?
(1 vote)
• No, there isn't a universally 'best' way. There may be a 'best' way in a given situation for a given problem, but even that will be a matter of opinion. It depends on how you prefer to process the information.
• If you factored it as 24x^5 = (6x^1)(4x^4), could you not factor the (4x^4) again with (2x^2)(2x^2)? Isn't this the best answer?
(1 vote)
• The problem asked for the product of 2 monomials. You did 3 monomials. It also asked you to pick the one that was correct, not do your own.

If it had asked you to create 2 monomial factors, there are more than one pair what would work. 24X^5 can be split into quite a few monomial factors that would work.
-- The 24 can split into 1 & 24; 2 & 12; 3 & 8; and 4 & 6.
-- The x^5 can be split into 1 & x^5; x & x^4; x^2 ^ x^3.
You can pair these options up in many ways to get 2 monomials factors of 24x^5. Without additional info that would restrict your options, no factor pair is necessarily better than another.

If you were asked to create 3 monomial factors, then again, there are multiple options that you could create. None are necessarily better/worse than another.

Hope this helps.