# Need some help with adding and subtracting polynomials

#### Rafael De La Ghetto

##### New member
Hey guys can someone tell me how to do these? I have a whole page of them and if someone can tell me how to do 1 or the answer I will be able to figure it out.

#1 Add: (4x<sup>3</sup> - 2x<sup>2</sup> + x + 4) + (9 - x<sup>5</sup> - x<sup>2</sup> + 4x)

#2 Subtract: (x - 3x<sup>4</sup> + 2x<sup>2</sup>) - (-x<sup>3</sup> + 4x<sup>6</sup>)

Thanks guys

#### jonboy

##### Full Member
Re: Need some help

Rafael De La Ghetto said:
Hey guys can someone tell me how to do these? I have a whole page of them and if someone can tell me how to do 1 or the answer I will be able to figure it out.

#1 Add: (4x<sup>3</sup> - 2x<sup>2</sup> + x + 4) + (9 - x<sup>5</sup> - x<sup>2</sup> + 4x)

#2 Subtract: (x - 3x<sup>4</sup> + 2x<sup>2</sup>) - (-x<sup>3</sup> + 4x<sup>6</sup>)

Thanks guys
Ok when adding polynomial you always add "like terms". This means you can only add/subtract terms which have the same exponent. For example if you have 3x^5 and x^4 you cannot add this because of the different exponents 5 and 4. If you had 3x^4 and 2x^4 and you added them your answer would be 5x^4.

So for the first:

-2x^2 + -x^2 = -3x^2

x + 4x = 5x

4 + 9 = 13

So your answer is: -x^5 + 4x^3 - 3x^2 + 5x + 13

For the second (as you can see there is no like terms so we just re-write it in descending order, the greater is the one w/the highest exponent in the term):

-4x^6 - 3x^4 + x^3 + 2x^2 + x

or x(-4x^5 -3x^3 + x^2 + 2x + 1)

I say you have learned a lot in just those two problems alone.

#### tkhunny

##### Moderator
Staff member
Rafael De La Ghetto said:
Hey guys can someone tell me how to do these?
(4 dogs + 3 cats + 2 elephants) + (1 dog + 1 cat + 1 giraffe)

It helps me get a feel for what "like terms" means.

#### Denis

##### Senior Member
Rafael, did you know that "de la" is French for "of the"?
Just wondering if you're making a joke

#### Rafael De La Ghetto

##### New member
Re: Need some help

jonboy said:
Rafael De La Ghetto said:
Hey guys can someone tell me how to do these? I have a whole page of them and if someone can tell me how to do 1 or the answer I will be able to figure it out.

#1 Add: (4x<sup>3</sup> - 2x<sup>2</sup> + x + 4) + (9 - x<sup>5</sup> - x<sup>2</sup> + 4x)

#2 Subtract: (x - 3x<sup>4</sup> + 2x<sup>2</sup>) - (-x<sup>3</sup> + 4x<sup>6</sup>)

Thanks guys
Ok when adding polynomial you always add "like terms". This means you can only add/subtract terms which have the same exponent. For example if you have 3x^5 and x^4 you cannot add this because of the different exponents 5 and 4. If you had 3x^4 and 2x^4 and you added them your answer would be 5x^4.

So for the first:

-2x^2 + -x^2 = -3x^2

x + 4x = 5x

4 + 9 = 13

So your answer is: -x^5 + 4x^3 - 3x^2 + 5x + 13

For the second (as you can see there is no like terms so we just re-write it in descending order, the greater is the one w/the highest exponent in the term):

-4x^6 - 3x^4 + x^3 + 2x^2 + x

or x(-4x^5 -3x^3 + x^2 + 2x + 1)

I say you have learned a lot in just those two problems alone.
Thanks man, that was easy to understand.

Denis said:
Rafael, did you know that "de la" is French for "of the"?
Just wondering if you're making a joke
Yea its supposed to be a joke. I couldnt think of a username so I took a name from a Fresh Prince of Bell Air episode

Thanks again for all the help guys.