Who came up with this theory?

No one knows but the theory is called Discriminant

When we divide x by x, don't we get x to the zero power?

Not exactly. x/x = 1 because that is just a fraction rule. 8/8 = 1, 8532/8532 = 1 and so on

How did we get the 3y^2 at the end? I got 3xy^2 as my answer. Did Mr.Sal get the 3y^2 because when he divided 42x and 14x, did the x's cancel out?

yep, variables can cencel out when dividing. x/x = 1, (x^2)/x = x and x/(x^2) = 1/x. then you can just plug in other exponents to make it work. It might even be easier to think of it with numbers. (2^5) / (2^3) = 2^2

What if you distributed L? Why do we not? Is it because it's a monomial?

Correct. There isn't anywhere to distribute it to because L and 14xy are both monomials: L(14xy) distributed would just be L14xy . Which doesn't actually change anything - it just makes the equation look a little more sloppy.

what is the area of a rectangle? it is base by height height 14xy and base 3y^2

A of a rect = length * width. I would use "height" and "base" when solving for the volume of an object (ex. cylinder) OR if you are solving for the area of a triangle. Hope that helps!

How do you find the area of a missing side of a shape? and how do you find the missing side of a triangle when given the area?

We divide the are from the given length (regarding the formula of area for a particular shape)

Main content

Integrated math 3

Course: Integrated math 3 > Unit 2

Lesson 1: Factoring monomials

Worked example: finding missing monomial side in area model

Name: Worked example: finding missing monomial side in area model
Uploaded: 2015-11-03T11:55:11Z
Description: Learn how to find the length of a rectangle using algebraic expressions, as Sal finds the length of a rectangle whose area is 42xy^3 and whose height is 14xy. Dive into dividing coefficients and variables to solve for length and uncover how dividing powers of 'y' can simplify your equation.

Google Classroom

Learn how to find the length of a rectangle using algebraic expressions, as Sal finds the length of a rectangle whose area is 42xy^3 and whose height is 14xy. Dive into dividing coefficients and variables to solve for length and uncover how dividing powers of 'y' can simplify your equation.

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byron
Posted 7 years ago. Direct link to byron's post “Who came up with this the...”
Who came up with this theory?
Button navigates to signup pageComment on byron's post “Who came up with this the...”
(7 votes)
Answer
- RJ
  Posted 7 years ago. Direct link to RJ's post “No one knows but the theo...”
  No one knows but the theory is called Discriminant
  Button navigates to signup page
  (7 votes)
Arbaaz Ibrahim
Posted 5 years ago. Direct link to Arbaaz Ibrahim's post “When we divide x by x, do...”
When we divide x by x, don't we get x to the zero power?
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(4 votes)
Answer
- Delta Whiskey
  Posted 2 years ago. Direct link to Delta Whiskey's post “Not exactly. x/x = 1 beca...”
  Not exactly. x/x = 1 because that is just a fraction rule. 8/8 = 1, 8532/8532 = 1 and so on
  Button navigates to signup page
  (2 votes)
Yaw Opoku-Afriyie
Posted 3 years ago. Direct link to Yaw Opoku-Afriyie's post “How did we get the 3y^2 a...”
How did we get the 3y^2 at the end? I got 3xy^2 as my answer. Did Mr.Sal get the 3y^2 because when he divided 42x and 14x, did the x's cancel out?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- loumast17
  Posted 3 years ago. Direct link to loumast17's post “yep, variables can cencel...”
  yep, variables can cencel out when dividing. x/x = 1, (x^2)/x = x and x/(x^2) = 1/x. then you can just plug in other exponents to make it work.
  
  It might even be easier to think of it with numbers. (2^5) / (2^3) = 2^2
  Button navigates to signup page
  (3 votes)
-RandomPerson-
Posted 6 years ago. Direct link to -RandomPerson-'s post “What if you distributed L...”
What if you distributed L?
Why do we not? Is it because it's a monomial?
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(3 votes)
Answer
- JeremiahJTReed
  Posted 6 years ago. Direct link to JeremiahJTReed's post “Correct. There isn't anyw...”
  Correct. There isn't anywhere to distribute it to because L and 14xy are both monomials:
  L(14xy) distributed would just be L14xy . Which doesn't actually change anything - it just makes the equation look a little more sloppy.
  Comment on JeremiahJTReed's post “Correct. There isn't anyw...”
  (3 votes)
Fernando B
Posted 8 months ago. Direct link to Fernando B's post “what is the area of a r...”
what is the area of a rectangle?
it is base by height
height 14xy and base 3y^2
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(2 votes)
Answer
- SunnyWolf
  Posted 5 months ago. Direct link to SunnyWolf's post “A of a rect = length * wi...”
  A of a rect = length * width. I would use "height" and "base" when solving for the volume of an object (ex. cylinder) OR if you are solving for the area of a triangle.
  
  Hope that helps!
  Button navigates to signup page
  (3 votes)
Panhamorakath You
Posted 3 years ago. Direct link to Panhamorakath You's post “How do you find the area ...”
How do you find the area of a missing side of a shape? and how do you find the missing side of a triangle when given the area?
Button navigates to signup pageComment on Panhamorakath You's post “How do you find the area ...”
(2 votes)
Answer
- Alexia
  Posted 3 years ago. Direct link to Alexia's post “We divide the are from th...”
  We divide the are from the given length (regarding the formula of area for a particular shape)
  Button navigates to signup page
  (2 votes)
strahmhoffman
Posted 2 months ago. Direct link to strahmhoffman's post “Do we need to specify tha...”
Do we need to specify that 14xy is not equal to 0 ?
Button navigates to signup pageComment on strahmhoffman's post “Do we need to specify tha...”
(1 vote)
Answer
aliah_vaiese_20
Posted 4 years ago. Direct link to aliah_vaiese_20's post “what if my area is 12y^2+...”
what if my area is 12y^2+21y^5 and im trying to find the width and length using factroring?
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(1 vote)
Answer
- Victor
  Posted 4 years ago. Direct link to Victor's post “You can extract 3y^2 from...”
  You can extract 3y^2 from both sides.
  12y^2+21y^5
  = 3y^2(7y^3 + 4)
  From there you factor it out and find out your y values.
  I hope this helped!
  Comment on Victor's post “You can extract 3y^2 from...”
  (1 vote)

Video transcript

- [Voiceover] So we have a rectangle right over here. Let's say that we know that its area is 42x times y to the third. So that is the area of the rectangle. And we also know that the height right over here is 14xy and what we want to do in this video is figure out what the length is going to be. And as you can imagine, it's going to be in algebraic terms. So I encourage you to pause the video and figure out what is the length going to be if this height is 14xy and the area is 42xy to the third. Well, how do you figure out area? You take your length, and I'll just use L for length. I'll put L in parentheses. So you take your length and you multiply it times your height. So let's multiply it times 14xy and that's going to give you your area. So that's going to give us our area of 42xy to the third power. So how do we solve for our length? Well, we can just divide both sides by 14xy. So let's do that. So, let's divide the left-hand side and the right-hand side by 14xy, 14xy. Now on the left-hand side, I'm multiplying by 14xy and dividing by 14xy, that's the same thing as just multiplying or dividing by one so that cancels out. So I'm just left with L or our length which is the whole point of dividing both sides by 14xy. And on the right-hand side, I can look at the coefficients first. I could say 42 divided by 14, and that's going to be three. Three, and then I could say well, x divided by x that's just going to be one, and then I have y to the third divided by y. y to the third divided by y, that is going to be y to the third divided by y is going to be y-squared. And then we're done. Our length is three y-squared. So our length is equal to three y-squared.