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## Integrated math 3

### Course: Integrated math 3>Unit 2

Lesson 3: Taking common factors

# Taking common factor: area model

The video explores taking common factors in algebra using an area model. It demonstrates how to find the greatest common monomial factor of terms and uses the area of a rectangle as a visual aid. By factoring out the length and width, you can better grasp the process of factoring polynomials.

## Want to join the conversation?

• How is x squared divisible into x cubed? I have been confused with this since the last video in this area. I have seen other explanations of this, but I still do not understand.
• x cubed is x*x*x. x squared is x*x. So you have x*x*x/x*x. You have 3 x's in the numerator and 2 in the denominator.

You can cancel out 2 x's in the top and 2 x's in the bottom. That leaves you with just 1 x remaining in the top.

Alternately, if the bases are the same, you can simply subtract the powers. x^3 / x^2. You can subtract 2 from 3 and that leaves you with x^1 or just x.
• I'm confused. How can x^2 be a part of the greatest common monomial facter? How does x^2 go into x^3 ? Shouldn't the greatest common monomial factor in this situation be 3x because x can go into all variables?
• I think you're confusing about division of exponent with same base. Rules of exponent state that a^m/a^n = a^(m-n).
So x^4 / x^2 = x^(4-2)= x^2
x^3 / x^2 =x^(3-2)=x^1 = x
x^2 / x^2= x^(2-2) = x^0 = 1
• At Sal says, "What are the non-prime factors of each of these numbers?" Why non-prime factors specifically?
• Sal is showing two different ways to find the greatest common factor.
The first way, at , he does prime factorization.
The second way, at , he uses non-prime factorization.
So if he didn't make the specification in the second example of "non-prime factors" he would just be repeating what he had shown at .
• When you have factored everything out, and get get (3x^2)(4x^2+2x+5), could you just add it up to get (3x^2)(11x^3), and then 33x^5?
• So I have a question...

How can area models and Diamond problems help you factor challenging expressions?
If you look at the video carefully, Sal does not use the area model to help you factor out the equation, he just uses it to show that (3x^2)(4x^2 + 2x + 5) = 12x^4 + 6x^3 + 15x^2.
• why x square by 3 divided by x square by 2 is equal x?
• Your words means x^2*3 / (x^2*2) = 3/2.

Did you mean x^3 (x cubed) / x^2 (x squared)? If yes, then...
x^3/x^2 = (x*x*x)/(x*x) = x
Reduce the fraction by dividing out common factors. 2 x's can be divided out leaving just x

• How is the least common of x is x^2
(1 vote)
• You are not finding LCM, you are finding GCF.
• I believe that that question is unfactorable