What are polynomials used for?

" Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example." Also, you might find this interesting "Engineering Careers. Aerospace engineers, chemical engineers, civil engineers, electrical engineers, environmental engineers, mechanical engineers and industrial engineers all need strong math skills. Their jobs require them to make calculations using polynomial expressions and operations."

why is it important to learn polynomials?

It is actually used in a lot of careers in the future, like engineering, finance, or other math-related fields.

How wouldn't it be -10y with the exponent of 2 if all the other numbers cncel out

It's actually -10y^2 as -7y^2+-3y^2 = -7y^2-3y^2= y^2(-7-3)= -10y^2

What method can I use to remember to put in my negative n positive sign , I’m having a little trouble with negative n positive.

- * - = + - * + = - + * + = + That's for multiplication rules. - * + is equal to + * - As for addition and subtraction, whichever sign's number is larger, they will take that sign. Example: -2 - (- 2) = -2 + 2 = 0 I hope this helped!

do you guys have an easier method for this lesson?

You may be over thinking this. Adding polynomials is the same as combining like terms. If you can combine like terms, then you can add polynomials. To subtract polynomials, you just need to remember to distribute the "minus" sign to all the terms in the polynomial being subtracted. Once you've done the distribution, you are back to combining like terms. Hope this helps.

for (3x+1)-(2x+3) we do 3x+1-2x-3 like -1(2x+3) is there video on khan academy explaining what's the fundamental behind this.

with -(2x+3), you can distribute the "-" itself: -(2x) -(+3) which basically says change all terms to their opposite sign, and creates -2x-3 Or, you can treat the "-" as -1. Remember "-x" is the same as "-1x". So, by changing the "-" to "-1", you are essentially doing the same thing. -1(2x+3) = -1(2x) -1(+3) = -2x-3 You get the same result using either approach. Hope this helps.

Sometimes in subtracting polynomials I just dont know when to put like a - or a +

I know! its hard to remember! sometimes i get confused between which negatives and positives to put and i mix up the signs! ive got an answer at this link explaining how to not get confused! :) https://www.khanacademy.org/video/solving-equations-with-the-distributive-property?qa_expand_key=ag5zfmtoYW4tYWNhZGVteXJACxIIVXNlckRhdGEiHWthaWRfODY4NDgzODk3NjM3NzY3MzkyNzk3MjMxDAsSCEZlZWRiYWNrGICAuZTJyoUKDA copy the whole link and it will take you there! hope this helped! :D

Main content

Algebra basics

Course: Algebra basics > Unit 7

Lesson 1: Adding & subtracting polynomials

Adding and subtracting polynomials review

CCSS.Math:

HSA.APR.A.1

HSA.APR.A

Google Classroom

Adding and subtracting polynomials is all about combining like terms. In this article, we review some examples and give you a chance for you to practice the skill yourself.

Adding and subtracting polynomials is an exercise in combining like terms. Let's walk through some examples.

Example 1

Simplify.

left parenthesis, 5, h, cubed, minus, 8, h, right parenthesis, plus, left parenthesis, minus, 2, h, cubed, minus, h, squared, minus, 2, h, right parenthesis

Rewrite without parentheses:

start color #11accd, 5, h, cubed, minus, 8, h, end color #11accd, start color #ca337c, minus, 2, h, cubed, minus, h, squared, minus, 2, h, end color #ca337c

Group like terms:

left parenthesis, start color #11accd, 5, h, cubed, end color #11accd, start color #ca337c, minus, 2, h, cubed, end color #ca337c, right parenthesis, start color #ca337c, minus, h, squared, end color #ca337c, plus, left parenthesis, start color #11accd, minus, 8, h, end color #11accd, start color #ca337c, minus, 2, h, end color #ca337c, right parenthesis

Simplify:

3, h, cubed, minus, h, squared, minus, 10, h

Want to see another example? Check out this video.

Example 2

Simplify.

left parenthesis, minus, w, cubed, plus, 8, w, squared, minus, 3, w, right parenthesis, minus, left parenthesis, 4, w, squared, plus, 5, w, minus, 7, right parenthesis

Rewrite without parentheses (being careful to distribute the negative):

start color #11accd, minus, w, cubed, plus, 8, w, squared, minus, 3, w, end color #11accd, start color #ca337c, minus, 4, w, squared, minus, 5, w, plus, 7, end color #ca337c

Group like terms:

start color #11accd, minus, w, cubed, end color #11accd, plus, left parenthesis, start color #11accd, 8, w, squared, end color #11accd, start color #ca337c, minus, 4, w, squared, end color #ca337c, right parenthesis, plus, left parenthesis, start color #11accd, minus, 3, w, end color #11accd, start color #ca337c, minus, 5, w, end color #ca337c, right parenthesis, start color #ca337c, plus, 7, end color #ca337c

Simplify:

minus, w, cubed, plus, 4, w, squared, minus, 8, w, plus, 7

Want to see another example? Check out this video.

Example 3

Express E, plus, F as a trinomial.

\begin{aligned} E &= 6c^2-2c-1 \\\\ F &= -4c^2+7c+5 \end{aligned}

E, plus, F, equals, left parenthesis, 6, c, squared, minus, 2, c, minus, 1, right parenthesis, plus, left parenthesis, minus, 4, c, squared, plus, 7, c, plus, 5, right parenthesis

Rewrite without parentheses and color code like terms:

start color #11accd, 6, c, squared, end color #11accd, start color #1fab54, minus, 2, c, end color #1fab54, start color #7854ab, minus, 1, end color #7854ab, start color #11accd, minus, 4, c, squared, end color #11accd, start color #1fab54, plus, 7, c, end color #1fab54, start color #7854ab, plus, 5, end color #7854ab

Group like terms:

start color #6495ed, left parenthesis, 6, minus, 4, right parenthesis, c, squared, end color #6495ed, plus, start color #28ae7b, left parenthesis, minus, 2, plus, 7, right parenthesis, c, end color #28ae7b, plus, start color #9d38bd, left parenthesis, minus, 1, plus, 5, right parenthesis, end color #9d38bd

Simplify:

2, c, squared, plus, 5, c, plus, 4

Want to see another example? Check out this video.

Practice

Problem 1

Current

Simplify.

left parenthesis, minus, 3, y, squared, minus, 5, y, minus, 2, right parenthesis, plus, left parenthesis, minus, 7, y, squared, plus, 5, y, plus, 2, right parenthesis

Want more practice? Check out these exercises:

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Hennessey Venom F5
Posted 6 years ago. Direct link to Hennessey Venom F5's post “What are polynomials used...”
What are polynomials used for?
Button navigates to signup pageComment on Hennessey Venom F5's post “What are polynomials used...”
(49 votes)
Answer
- Mina
  Posted 5 years ago. Direct link to Mina's post “" Since polynomials are u...”
  " Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example."
  
  Also, you might find this interesting "Engineering Careers. Aerospace engineers, chemical engineers, civil engineers, electrical engineers, environmental engineers, mechanical engineers and industrial engineers all need strong math skills. Their jobs require them to make calculations using polynomial expressions and operations."
  Comment on Mina's post “" Since polynomials are u...”
  (119 votes)
mcallisterjrrandy
Posted 6 years ago. Direct link to mcallisterjrrandy's post “I always forget to put th...”
I always forget to put the negative sign in front of the number if there is one and i get it wrong cause of that
Button navigates to signup pageComment on mcallisterjrrandy's post “I always forget to put th...”
(37 votes)
Answer
- michaelsunheheheha
  Posted 4 months ago. Direct link to michaelsunheheheha's post “same”
  same
  Comment on michaelsunheheheha's post “same”
  (5 votes)
2268ratz
Posted 3 years ago. Direct link to 2268ratz's post “why is it important to le...”
why is it important to learn polynomials?
Button navigates to signup pageComment on 2268ratz's post “why is it important to le...”
(16 votes)
Answer
- ana
  Posted 3 years ago. Direct link to ana's post “It is actually used in a ...”
  It is actually used in a lot of careers in the future, like engineering, finance, or other math-related fields.
  Comment on ana's post “It is actually used in a ...”
  (7 votes)
sohia paul
Posted 3 years ago. Direct link to sohia paul's post “What method can I use to ...”
What method can I use to remember to put in my negative n positive sign ,
I’m having a little trouble with negative n positive.
Button navigates to signup pageComment on sohia paul's post “What method can I use to ...”
(5 votes)
Answer
- Victor
  Posted 3 years ago. Direct link to Victor's post “- * - = + - * + = - + * +...”
  - * - = +
  - * + = -
  + * + = +
  That's for multiplication rules. - * + is equal to + * -
  As for addition and subtraction, whichever sign's number is larger, they will take that sign.
  Example: -2 - (- 2) = -2 + 2 = 0
  I hope this helped!
  Comment on Victor's post “- * - = + - * + = - + * +...”
  (14 votes)
nyrielcharley
Posted 6 years ago. Direct link to nyrielcharley's post “How wouldn't it be -10y w...”
How wouldn't it be -10y with the exponent of 2 if all the other numbers cncel out
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- victoriamathew12345
  Posted 2 years ago. Direct link to victoriamathew12345's post “It's actually -10y^2 as -...”
  It's actually -10y^2 as -7y^2+-3y^2 = -7y^2-3y^2= y^2(-7-3)= -10y^2
  Button navigates to signup page
  (5 votes)
emmanuella.otu
Posted 8 months ago. Direct link to emmanuella.otu's post “why does some of the exer...”
why does some of the exercises keep telling me to start over, when i have done it up to two to three times?
Button navigates to signup pageComment on emmanuella.otu's post “why does some of the exer...”
(7 votes)
Answer
- benjaminn.ku
  Posted 11 days ago. Direct link to benjaminn.ku's post “I think he's right, but, ...”
  I think he's right, but, don't push start over, unless you want to start over. lol
  Button navigates to signup page
  (1 vote)
Dryzta ovince
Posted 2 years ago. Direct link to Dryzta ovince's post “do you guys have an easie...”
do you guys have an easier method for this lesson?
Button navigates to signup pageComment on Dryzta ovince's post “do you guys have an easie...”
(5 votes)
Answer
- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “You may be over thinking ...”
  You may be over thinking this.
  Adding polynomials is the same as combining like terms. If you can combine like terms, then you can add polynomials.
  
  To subtract polynomials, you just need to remember to distribute the "minus" sign to all the terms in the polynomial being subtracted. Once you've done the distribution, you are back to combining like terms.
  
  Hope this helps.
  Button navigates to signup page
  (9 votes)
Alex
Posted 3 years ago. Direct link to Alex's post “Sometimes in subtracting ...”
Sometimes in subtracting polynomials I just dont know when to put like a - or a +
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- 𝘽𝘼𝙏𝙈𝘼𝙉
  Posted 3 years ago. Direct link to 𝘽𝘼𝙏𝙈𝘼𝙉's post “I know! its hard to remem...”
  I know! its hard to remember! sometimes i get confused between which negatives and positives to put and i mix up the signs! ive got an answer at this link explaining how to not get confused! :)
  
  https://www.khanacademy.org/video/solving-equations-with-the-distributive-property?qa_expand_key=ag5zfmtoYW4tYWNhZGVteXJACxIIVXNlckRhdGEiHWthaWRfODY4NDgzODk3NjM3NzY3MzkyNzk3MjMxDAsSCEZlZWRiYWNrGICAuZTJyoUKDA
  
  copy the whole link and it will take you there! hope this helped! :D
  Comment on 𝘽𝘼𝙏𝙈𝘼𝙉's post “I know! its hard to remem...”
  (10 votes)
2025.sophia.f
Posted 5 days ago. Direct link to 2025.sophia.f's post “slay”
slay
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(8 votes)
Answer
frost fzz
Posted a year ago. Direct link to frost fzz's post “for (3x+1)-(2x+3) we do 3...”
for (3x+1)-(2x+3)
we do 3x+1-2x-3 like -1(2x+3)
is there video on khan academy explaining what's the fundamental behind this.
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kim Seidel
  Posted a year ago. Direct link to Kim Seidel's post “with -(2x+3), you can dis...”
  with -(2x+3), you can distribute the "-" itself: -(2x) -(+3) which basically says change all terms to their opposite sign, and creates -2x-3
  
  Or, you can treat the "-" as -1. Remember "-x" is the same as "-1x". So, by changing the "-" to "-1", you are essentially doing the same thing.
  -1(2x+3) = -1(2x) -1(+3) = -2x-3
  
  You get the same result using either approach.
  Hope this helps.
  Button navigates to signup page
  (7 votes)