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! :)

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!

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.

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!

i don't get the last two

6) just asks for the prime factorization, so 22 = 2 • 11, so just add that to the variables to get 2 • 11 x • y • y. Prime factorization helps us find GCF and LCM 7) this is popular way to create problems, note that A = l w, so we can set an equation 24 x^3 = 4 x^2 w divide both sides by 4 x^2, we get 4 • 6 xxx/4 xx and canceling we get 6x.

i hate khan acadeemy no ofence but i dont learn a thing

you might be suffering from missing fundamentals. Before approaching a unit, try and see what its prerequisites are first.

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!]

Want to join the conversation?

Sort by:

Jannete
Posted 5 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.
Button navigates to signup pageButton navigates to signup page
(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....”
  (25 votes)
Cassandra Lehnerd
Posted 4 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?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kathryn Smith
  Posted 4 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
  (11 votes)
Katelyn Friis
Posted 4 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?
Button navigates to signup pageButton navigates to signup page
(5 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 6 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.
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kim Seidel
  Posted 6 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.
  Button navigates to signup page
  (5 votes)
tesa7044
Posted 20 days ago. Direct link to tesa7044's post “easy”
easy
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
coco1max2
Posted 3 years ago. Direct link to coco1max2's post “philosophically why do we...”
philosophically why do we simplify?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
Joseph Gonzalez
Posted 5 years ago. Direct link to Joseph Gonzalez's post “So a simple way of doing ...”
So a simple way of doing it is by dividing the total by the number given and then subtracting the exponent given from the total and then what you get is your answer?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Jonathan
  Posted 2 years ago. Direct link to Jonathan's post “Technically, yes. A bette...”
  Technically, yes. A better way to think about it is to think that you are dividing the coefficients and the exponents separately.
  
  For example, let's say we have to find A in (A)4x^2=8x^3. We would divide both sides by 4x^2. First, divide the coefficients: 8/4=2. Then, divide the exponents: x^3/x^2=x*x*x/x*x=x. Multiplying our two results together will give us our answer: 2x.
  
  Hope this helps!
  
  Jonathan Myung
  Button navigates to signup page
  (1 vote)
sgonz090
Posted 5 months ago. Direct link to sgonz090's post “How can understand this b...”
How can understand this better?
Button navigates to signup pageComment on sgonz090's post “How can understand this b...”
(1 vote)
Answer
- im a vampire
  Posted 5 months ago. Direct link to im a vampire's post “as i tell myself practice...”
  as i tell myself practice makes progress not perfect because you cant be perfect or you'll die trying!
  Button navigates to signup page
  (3 votes)
MenthuPlayz
Posted 6 years ago. Direct link to MenthuPlayz's post “i don't get the last two”
i don't get the last two
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “6) just asks for the prim...”
  6) just asks for the prime factorization, so 22 = 2 • 11, so just add that to the variables to get 2 • 11 x • y • y. Prime factorization helps us find GCF and LCM
  7) this is popular way to create problems, note that A = l w, so we can set an equation
  24 x^3 = 4 x^2 w divide both sides by 4 x^2, we get 4 • 6 xxx/4 xx and canceling we get 6x.
  Comment on David Severin's post “6) just asks for the prim...”
  (4 votes)
Italian Pizza
Posted 8 months ago. Direct link to Italian Pizza's post “i hate khan acadeemy no o...”
i hate khan acadeemy no ofence but i dont learn a thing
Button navigates to signup pageComment on Italian Pizza's post “i hate khan acadeemy no o...”
(0 votes)
Answer
- Marci Lustra
  Posted 7 months ago. Direct link to Marci Lustra's post “you might be suffering fr...”
  you might be suffering from missing fundamentals. Before approaching a unit, try and see what its prerequisites are first.
  Button navigates to signup page
  (10 votes)