Need some help with adding and subtracting polynomials

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Rafael De La Ghetto

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Jul 7, 2006
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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
 
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
Click to expand...

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

It helps me get a feel for what "like terms" means.
 
Rafael, did you know that "de la" is French for "of the"?
Just wondering if you're making a joke 8-)
 
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
Click to expand...

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. :)
Click to expand...

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 8-)
Click to expand...

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 :p

Thanks again for all the help guys.
 
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