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### Course: Algebra 1 (Eureka Math/EngageNY) > Unit 4

Lesson 1: Topic A: Lessons 1-2: Factoring monomials- Intro to factors & divisibility
- Intro to factors & divisibility
- Factors & divisibility
- 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

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# Worked example: finding the missing monomial factor

Follow along as Sal works an example to show you how to factor monomials by isolating variables in equations. Learn how to use exponent properties to rewrite complex expressions and get a firm grasp on the crucial role that coefficients and exponents play in this process. This knowledge will empower you to solve for unknown factors in any monomial equation.

## Want to join the conversation?

- what does this all mean? What are non-fractional co-efficients?(5 votes)
- Non-fractional co-efficients? A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x^y). Non fractional means it's not a fraction.(22 votes)

- But isn’t dividing by a variable a big no no?

At2:57, why would it be different if the coefficient or exponent were fractional?(7 votes) - What grade level is this considered?(3 votes)
- This video was under the Algebra 2 course, polynomial factorization, then factoring monomials. I'm taking it in Middle school. So I hope this helped(7 votes)

- I recently came across a question about how to solve 16x^2-32x+15 . Would it make more sense to use quadratic formula or to think about it like what multiplies to 16*15 and what adds to -32? And why you think that this is easier?(2 votes)
- I would use factoring. The factors you need are: -12 and -20.

The polynomial has some large numbers. If you use the quadratic formula you can get even larger numbers, particularly inside the radical. Then, you are faced with simplifying the radical.(6 votes)

- 0:34What are the instances when dividing by the variable is okay and what are the instances when doing so would not be okay because it would be equivalent to cancelling out possible results?(1 vote)
- When your variable can equal zero, you can't divide by it (as division by zero isn't defined). Here too, division removes a solution of x (x=0) but as finding x isn't our goal anyway, we can freely divide.(3 votes)

- I have a question why thus this algebra so important.(2 votes)
- At0:30, Sal writing the -10x^3 under both, but shouldnt it be -10x^3 / -10x^3 AND (F) / -10x^3 ? Thanks(1 vote)
- No because these two terms are being multiplied together rather than added. He did not have to use parentheses to separate them because they are all one term, but it is easier to see. If they were added instead of multiplied, then the opposite would be to subtract and that is a different problem.(2 votes)

- Do we need to specify that -10x^3 is not equal to 0 ?(1 vote)
- why does sal make everything hard(1 vote)
- How do you find the missing factor? and how do you find the factors of a Monomial?(1 vote)
- 1)We do it the same way as we do it for natural numbers.

eg. Find another factor of 35

35- 5 and ?

Ans. 35/5 i.e.7

2) Let me explain with an example,

Factors of 8x^3 are-

>2x^2 and 4x

>x, 2x and 4x etc(0 votes)

## Video transcript

- [Voiceover] So we have
negative 30x to the fifth is equal to negative 10x
to the third, times F. And I encourage you to pause this video and see if you can figure
out what F is going to be. Well, the way that we can tackle it, we could just isolate the F
on the right-hand side here if we divide by negative 10x to the third. So we might say, well, we want to divide this side by negative 10x to the third, but if we want the equality to be true, if we want the left side
to stay being the same as the right side, whatever we do with the right side we have to do to the left side as well. So we have to divide the left side by negative 10x to the third. And then what does that leave us with? Well, on the right-hand side, up top we're multiplying by
negative 10x to the third, and then we're dividing by
negative 10x to the third, well, multiplying by something and then dividing by that same thing is the same thing as
just multiplying by one, or one way to think about
it, they just cancel out. So we are just going to be left with an F. We're going to be left an
F on the right-hand side. And there's the whole point,
we wanted to solve for F. And on the left-hand side, we can first look at the coefficients. We could say negative 30 divided by, negative 30 divided by negative 10 is positive three. So that's going to be three. And then x to the fifth power divided by x to the third power, well that's going to be x-squared, x-squared. You could either think of
it in terms of our exponent properties, we would
subtract these two exponents, x to the five minus
three, which is x-squared or you could say up on top that's x times x times x times x times x. Did I say that right? Five x's. You could do it as x, let me do to that, on top, you have x to the fifth which is this. I also like to remind myself why the exponent properties even work. And then on the denominator, on the denominator you have x times x times x and these three x's are going to cancel and you're just going to
be left with x times x which is just x-squared. So you get F is equal to three x-squared so you could write, we could write that
negative 30x to the fifth is equal to, is equal to the negative 10x to the third times F and now we know that F is three x-squared. Three x-squared. And so another way to
describe what's going on in this equation, we could say that negative 30x to the fifth
is divisible by either one of these factors. That negative 30x to the
fifth is divisible by negative 10x to the third or we could say negative 30x to the fifth is divisible by three x-squared or we could say that three x-squared is a factor of negative 30x to the fifth. And the way that we can
make these claims about factor and divisibility
is we're dealing with non-fractional coefficients
right over here and we're also dealing with
non-fractional exponents right over here so that's why we're saying,
hey, these are factors, this yellow thing and this magenta thing, factors of this blue thing or this blue thing is divisible
by either one of these.