i need help with this i have already tried a lot but i just don't get it.

Let me see if I can help. One way to look at factorizing monomials is pulling them apart into their basic parts. Like you had a peanut butter and jelly sandwich. Pulling that into its basic parts, you could get bread times bread times peanut butter times jelly. That would be its complete factorization. Now for a monomial Say you have a monomial (or one term) that is 24x^2. There are a few ways to factor this. One example would be: (4x)(6x) This is not a complete factorization, but it is still a valid way to factorize it. Another way to do it would be (3)(8x^2) Its complete factorization would be 2 times 2 times 2 times 3 times x times x. When factoring, you just need to make sure that when you preform all the operations, they still come out to be the original number. Like I need to make sure (4x)(6x) = 24x^2. Let's check. 4 times 6 equals 24, and x times x equals x^2. Those two multiplied together equals 24x^2. I hope that helped! :)

You don't earn energy points on the articles, but you guys do it anyway. Good job! Keep it up.

yeah, i mean i noticed its just summary material-not new stuff

I am still confused on how to tell if it is a monomial or not. Can you help me?

A monomial is a single term polynomial, with a non-negative integer exponent. Typically each term in a polynomial is separated by addition/subtraction.

I'm having a hard time understanding how to find the width of the rectangle,how should i go about finding the width of a rectangle?

Length times width equals area. So to find width, you would divide the area by length. hope that helps!

If it has 1 term, it is a monomial. If it has 2 terms, it is a binomial. 3 terms or more is a polynomial.

Slight clarification: All of them are polynomials. The classification as monomial, binomial, or trinomial just gives more descriptive information about the polynomial. You omitted trinomial from you list. It has 3 terms.

How can understand this better?

as i tell myself practice makes progress not perfect because you cant be perfect or you'll die trying!

Why you don't answer my questions

I don't know what you mean. This is your 1st question and this is a response to that question. So your question is answered. Try posting questions about the lesson when you don't understand something. Be specific about what you don't understand and you will likely get a response. Other KhanAcademy users respond to questions in their spare time to help people learn.

Main content

Algebra 2

Course: Algebra 2 > Unit 3

Lesson 1: Factoring monomials

Factoring monomials

Google Classroom

Learn how to completely factor monomial expressions, or find the missing factor in a monomial factorization.

What you should be familiar with before this lesson

A monomial is an expression that is the product of constants and nonnegative integer powers of x, like 3, x, squared. A polynomial is a sum of monomials, like 3, x, squared, plus, 6, x, minus, 1.

If A, equals, B, dot, C, then B and C are factors of A, and A is divisible by B and C. To review this material, check out our article on Factoring and divisibility.

What you will learn in this lesson

In this lesson, you will learn how to factor monomials. You will use what you already know about factoring integers to help you in this quest.

Introduction: What is monomial factorization?

To factor a monomial means to express it as a product of two or more monomials.

For example, below are several possible factorizations of 8, x, start superscript, 5, end superscript.

8, x, start superscript, 5, end superscript, equals, left parenthesis, 2, x, squared, right parenthesis, left parenthesis, 4, x, cubed, right parenthesis
8, x, start superscript, 5, end superscript, equals, left parenthesis, 8, x, right parenthesis, left parenthesis, x, start superscript, 4, end superscript, right parenthesis
8, x, start superscript, 5, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 2, x, right parenthesis, left parenthesis, 2, x, right parenthesis, left parenthesis, x, squared, right parenthesis

Notice that when you multiply each expression on the right, you get 8, x, start superscript, 5, end superscript.

[I'd like to see the multiplication, please!]

Reflection question

Andrei, Amit and Andrew were each asked to factor the term 20, x, start superscript, 6, end superscript as the product of two monomials. Their responses are shown below.

Andrei			Amit			Andrew
20, x, start superscript, 6, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 10, x, start superscript, 5, end superscript, right parenthesis			20, x, start superscript, 6, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, 5, x, cubed, right parenthesis			20, x, start superscript, 6, end superscript, equals, left parenthesis, 20, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis

1) Which of the students factored 20, x, start superscript, 6, end superscript correctly?

[I need help!]

Completely factoring monomials

Review: integer factorization

To factor an integer completely, we write it as a product of primes.

For example, we know that 30, equals, 2, dot, 3, dot, 5.

And now to monomials...

To factor a monomial completely, we write the coefficient as a product of primes and expand the variable part.

For example, to completely factor 10, x, cubed, we can write the prime factorization of 10 as 2, dot, 5 and write x, cubed as x, dot, x, dot, x. Therefore, this is the complete factorization of 10, x, cubed:

10, x, cubed, equals, 2, dot, 5, dot, x, dot, x, dot, x

Check your understanding

2) Which of the following is the complete factorization of 6, x, squared?

[I need help!]

3) Which of the following is the complete factorization of 14, x, start superscript, 4, end superscript?

(Choice A)
14, dot, x, squared, dot, x, squared
(Choice B)
2, dot, 7, dot, x, squared, dot, x, squared
(Choice C)
14, dot, x, dot, x, dot, x, dot, x
(Choice D)
2, dot, 7, dot, x, dot, x, dot, x, dot, x

[I need help!]

Finding missing factors of monomials

Review: integer factorization

Suppose we know that 56, equals, 8, b for some integer b. How can we find the other factor?

Well, we can solve the equation 56, equals, 8, b for b by dividing both sides of the equation by 8. The missing factor is 7.

And now to monomials...

We can extend these ideas to monomials. For example, suppose 8, x, start superscript, 5, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, C, right parenthesis for some monomial C. We can find C by dividing 8, x, start superscript, 5, end superscript by 4, x, cubed:

$\begin{aligned}8x^5&=(4x^3)(C)\\ \\ \dfrac{8x^5}{4x^3}&=\dfrac{(4x^3)(C)}{4x^3}&&\small{\gray{\text{Divide both sides by }4x^3}}\\ \\\\\\ 2x^2&=C&&\small{\gray{\text{Simplify with properties of exponents}}} \end{aligned}$

[How did you divide here?]

We can check our work by showing that the product of 4, x, cubed and 2, x, squared is indeed 8, x, start superscript, 5, end superscript.

$\begin{aligned}(\purpleC{4}\tealD {x^3})(\purpleC{2}\tealD{x^2})&=\purpleC 4\cdot \purpleC{2}\cdot \tealD {x^3}\cdot \tealD{x^2}\\ \\ &=\purpleC{8}\tealD{x^5} \end{aligned}$

Check your understanding

4) Find the missing factor B that makes the following equality true.

28, x, start superscript, 5, end superscript, equals, left parenthesis, B, right parenthesis, left parenthesis, 7, x, right parenthesis

(Choice A)
4, x, start superscript, 4, end superscript
(Choice B)
4, x, start superscript, 5, end superscript
(Choice C)
21, x, start superscript, 4, end superscript
(Choice D)
21, x, start superscript, 5, end superscript

[I need help!]

5) Find the missing factor C that makes the following equality true.

40, x, start superscript, 9, end superscript, equals, left parenthesis, C, right parenthesis, left parenthesis, 4, x, cubed, right parenthesis

C, equals

[I need help!]

A note about multiple factorizations

Consider the number 12. We can write four different factorizations of this number.

12, equals, 2, dot, 6
12, equals, 3, dot, 4
12, equals, 12, dot, 1
12, equals, 2, dot, 2, dot, 3

However, there is only one prime factorization of the number 12, i.e. 2, dot, 2, dot, 3.

The same idea holds with monomials. We can factor 18, x, cubed in many ways. Here are a few different factorizations.

18, x, cubed, equals, 2, dot, 9, dot, x, cubed
18, x, cubed, equals, 3, dot, 6, dot, x, dot, x, squared
18, x, cubed, equals, 2, dot, 3, dot, 3, dot, x, cubed

Yet there is only one complete factorization!

18, x, cubed, equals, 2, dot, 3, dot, 3, dot, x, dot, x, dot, x

Challenge problems

6*) Write the complete factorization of 22, x, y, squared.

22, x, y, squared, equals

[I need help!]

7*) The rectangle below has an area of 24, x, cubed square meters and a length of 4, x, squared meters.

What is the width of the rectangle?

start text, W, i, d, t, h, end text, equals

meters

[I need help!]

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Jannete
Posted 6 years ago. Direct link to Jannete's post “i need help with this i h...”
i need help with this i have already tried a lot but i just don't get it.
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(11 votes)
Answer
- LarissaAnne
  Posted 4 years ago. Direct link to LarissaAnne's post “Let me see if I can help....”
  Let me see if I can help.
  
  One way to look at factorizing monomials is pulling them apart into their basic parts. Like you had a peanut butter and jelly sandwich. Pulling that into its basic parts, you could get bread times bread times peanut butter times jelly. That would be its complete factorization.
  
  Now for a monomial
  
  Say you have a monomial (or one term) that is 24x^2. There are a few ways to factor this. One example would be: (4x)(6x) This is not a complete factorization, but it is still a valid way to factorize it. Another way to do it would be (3)(8x^2) Its complete factorization would be 2 times 2 times 2 times 3 times x times x.
  
  When factoring, you just need to make sure that when you preform all the operations, they still come out to be the original number. Like I need to make sure (4x)(6x) = 24x^2. Let's check. 4 times 6 equals 24, and x times x equals x^2. Those two multiplied together equals 24x^2.
  
  I hope that helped! :)
  Comment on LarissaAnne's post “Let me see if I can help....”
  (27 votes)
Cassandra Lehnerd
Posted 5 years ago. Direct link to Cassandra Lehnerd's post “I'm having a hard time un...”
I'm having a hard time understanding how to find the width of the rectangle,how should i go about finding the width of a rectangle?
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(5 votes)
Answer
- Kathryn Smith
  Posted 5 years ago. Direct link to Kathryn Smith's post “Length times width equals...”
  Length times width equals area. So to find width, you would divide the area by length.
  hope that helps!
  Button navigates to signup page
  (12 votes)
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I'm so glad that he went into more detail with more videos. Because in the first video I was so lost lol.
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Neon Froggie
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You don't earn energy points on the articles, but you guys do it anyway. Good job! Keep it up.
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- Forever Learner
  Posted 2 months ago. Direct link to Forever Learner's post “yeah, i mean i noticed it...”
  yeah, i mean i noticed its just summary material-not new stuff
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Katelyn Friis
Posted 5 years ago. Direct link to Katelyn Friis's post “I am still confused on ho...”
I am still confused on how to tell if it is a monomial or not. Can you help me?
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(6 votes)
Answer
- Quinn
  Posted 4 years ago. Direct link to Quinn's post “A monomial is a single te...”
  A monomial is a single term polynomial, with a non-negative integer exponent.
  
  Typically each term in a polynomial is separated by addition/subtraction.
  Comment on Quinn's post “A monomial is a single te...”
  (6 votes)
obiudeozo0
Posted 10 months ago. Direct link to obiudeozo0's post “If it has 1 term, it is a...”
If it has 1 term, it is a monomial. If it has 2 terms, it is a binomial. 3 terms or more is a polynomial.
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(2 votes)
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- Kim Seidel
  Posted 10 months ago. Direct link to Kim Seidel's post “Slight clarification: Al...”
  Slight clarification: All of them are polynomials. The classification as monomial, binomial, or trinomial just gives more descriptive information about the polynomial. You omitted trinomial from you list. It has 3 terms.
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  (9 votes)
Stephanie Gonzalez
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How can understand this better?
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- im a vampire
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  as i tell myself practice makes progress not perfect because you cant be perfect or you'll die trying!
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Why you don't answer my questions
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- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “I don't know what you mea...”
  I don't know what you mean. This is your 1st question and this is a response to that question. So your question is answered.
  
  Try posting questions about the lesson when you don't understand something. Be specific about what you don't understand and you will likely get a response. Other KhanAcademy users respond to questions in their spare time to help people learn.
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this helped a lot but is there anyway to understand it better
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  search Youtube for extra explanations
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