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## Algebra 2

### Course: Algebra 2 > Unit 3

Lesson 1: Factoring monomials- Introduction to factoring higher degree polynomials
- Introduction to factoring higher degree monomials
- Which monomial factorization is correct?
- Worked example: finding the missing monomial factor
- Worked example: finding missing monomial side in area model
- Factoring monomials
- Factor 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?(9 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.(23 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?(8 votes)
- yes a monomial times a monomial will be a monomial and a polynomial times a polynomial is a polynomial(8 votes)

- i have no idea what im doing right now(7 votes)
- Foil I don't understand what that mean can you please help me?(3 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)

- 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)

- 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.(4 votes)

- i dont understand any of this.(3 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.(2 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?(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.(2 votes)

- 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.(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.