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### Course: Algebra (all content) > Unit 10

Lesson 11: Factoring monomials- Which monomial factorization is correct?
- Factoring monomials
- Worked example: finding the missing monomial factor
- Worked example: finding missing monomial side in area model
- Factor monomials
- Greatest common factor of monomials
- Greatest common factor of monomials
- Greatest common factor of monomials

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# 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?(10 votes)
- 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.(28 votes)

- will the product of two monomials always be a monomial, on the same note will the product of two polynomials always be a polynomial?(9 votes)
- yes a monomial times a monomial will be a monomial and a polynomial times a polynomial is a polynomial(9 votes)

- i have no idea what im doing right now(9 votes)
- Foil I don't understand what that mean can you please help me?(4 votes)
- FOIL is an acronym to try and help students remember how to multiply 2 binomials. It is explained in the video at this link: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/multiplying-binomials

Hope this helps.(5 votes)

- there are many ways yes but is there a best way?(2 votes)
- 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.(5 votes)

- what is monomial(2 votes)
- 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!(4 votes)

- i dont understand any of this.(3 votes)
- Factorization is when you split a mathematical figure into 2 or more parts that when multiplied, will give you the original number that you factorized.(1 vote)

- Help i dont understand disss(2 votes)
- yo ngl that explanation was not good im still confused(1 vote)
- Each way is correct, there is more than one way to factor this term correctly.(3 votes)

- Does it matter if factored forms of polynomials (or monomials) are in standard form or not, like:

(4x)(6x^4) or (6x^4)(4x)

Is it simply a style thing or does standard form only apply to the polynomials in their complete form?

Thank you so much for your time!(1 vote)- I believe it isn't strictly required (By the commutative of multiplication), but you are encouraged to do so.(2 votes)

## Video transcript

- "Theodore and Claire
were each asked to factor "the term 24 x to the
fifth as the product of "two monomials. "Their responses are shown below." So Theodore factored 24 x to the fifth as being equal to eight x third, times three x squared, and Claire factored 24 x to the fifth as being equal to four x times six x to the fourth. And then they ask us,
"Which of the students "factored 24 x to the fifth correctly?" So I encourage you,
pause the video and see if you can figure this out. Which of them factored it correctly? All right, now let's
first look at Theodore. So he factored it into
these two monomials, eight x to the third and three x squared. Well, let's just see,
if we were to multiply these two things, do we
get 24 x to the fifth? So if you multiply eight times three, you do indeed get 24. And then all you have to do is multiply the x terms, or the powers of x. You have x to the third times x squared, that indeed does equal x to the fifth. So Theodore did factor
it correctly, this is one factorization, I guess you would say, of 24 x to the fifth. Now let's look at Claire. So Claire, if we were
taking just the coefficient, four times six is indeed equal to 24. And then if we were to
look at the powers of x we have x to the first power here, times x to the fourth power,
which is going to be x to the fifth power. So Claire also factored it correctly. And this just goes to
show you that there's more than one possible factorization of a monomial like 24 x to the fifth. I could come up with another one. I could write something like 24 x to the fifth, I could say that that is 12 x, to the third, times, what
would have to be left? 12 times two is 24, so two x squared. That's another possible factorization. So clearly there's more than one way to factor this monomial
into two other monomials.