Divison of polynomials - remainder therom (2 Viewers)

[bored of sc]

Divison of polynomials - LONG DIVISION

Could someone please give me an explanation of this... thanks... I suck at long divsion... *gets sad*

 

[namburger]

if a polynomial P(x) is divided by (x-a), then p(a) is its remainder

 

[Slidey]

Moreover, if (x-a) is one its roots, the remainder, p(a), is equal to zero.

 

[bored of sc]

if a polynomial P(x) is divided by (x-a), then p(a) is its remainder

sorry, I just meant the divison of polynomials, not the remainder therom...

 

[lyounamu]

sorry, I just meant the divison of polynomials, not the remainder therom...

You do it one by one. What I mean by "one by one" is that you use the square root-look-alike method to solve it.

Look at either Fitzpatrick or Cambridge. They will explain to you how you can solve this. This is quite easy to understand. Good luck.

 

[selablad]

sorry, I just meant the divison of polynomials, not the remainder therom...

okay...I had no idea there was even such a thing as division of polynomials, but I just taught myself the basics so I could help a very helpful BOS member...sorry if this is wrong!

okay. these are the steps (I'll do it with an example):

dammit, I have no idea how to format this, pen and paper would have been better, I'm sorry!

1. write it out (the long division)

____________-
2x - 5 ) 2x³ - 9x² + 0x + 15


2. consider only the first terms of each function (2x and 2x³)

what do you have to do to 2x to give 2x³? answer: x x²

write that in the first spot (above the 2x³)


3. now multiply the "top" bit (the x²) by what you're dividing by (2x - 5)

and write that underneath, keeping like terms under like terms:

__x²____________
2x - 5 ) 2x³ - 9x² + 0x + 15
2x³ - 5x²


4. subtract these from each other, so that the bottom reads "0 - 4x²


5. now, what do you have to do to 2x to get -4x²? answer: x -2x

write this on the top line, in line with the -4x²

also carry down the 0x

__x² - 2x____________
2x - 5 ) 2x³ - 9x² + 0x + 15
2x³ - 5x²
- 4x² + 0x


6. now multiply the next "top" bit - ie the -2x, and write this under the 4x² + 0x, you get -4x² + 10x

subtract these and you get -10x


7. what do you have to do to 2x to get -10x? answer: -5. write this on the top line, in line with the -10x.

carry down the + 15

multiply 2x - 5 by - 5, and write it underneath


__x² - 2x - 5________
2x - 5 ) 2x³ - 9x² + 0x + 15
2x³ - 5x²
- 4x² + 0x
- 4x² + 10x
-10x + 15
-10x + 25
-10

a remainder of -10!!


FINALLY:

put the remainder over the divisor: -10/(2x - 5)

and add the top line (x² - 2x - 5) to the remainder thing (-10/(2x - 5)

and yeah, that's the answer

 

[bored of sc]

thank you so much, that's so kind of you learning all that for my benefit - wow, well done too: for teaching yourself so easily

there's a typing error on the attachment, but don't worry it only left the 2 off the x³ so nothing significant

 

[agua.fuego]

okay...I had no idea there was even such a thing as division of polynomials, but I just taught myself the basics so I could help a very helpful BOS member...sorry if this is wrong!
...
and yeah, that's the answer

Wow... that is pure skill... you TAUGHT YOURSELF THAT?
*lies down in shock*
That is absolutely amazing.

I don't do maths. That's why it is so - WOW - to me.

 

[Devouree]

okay...I had no idea there was even such a thing as division of polynomials, but I just taught myself the basics so I could help a very helpful BOS member...sorry if this is wrong!

okay. these are the steps (I'll do it with an example):

dammit, I have no idea how to format this, pen and paper would have been better, I'm sorry!

My respect for you just goes up and up... :uhhuh: mainly because typing that would have taken... too long to bother calculating, and because you actually taught yourself just for him

 

[Aerath]

Bloody hell selablad. Ultimate respect.

 

[selablad]

Well, he said he believed in karma. I was just making sure it came back to him

 

[bored of sc]

cool, cool, cool - this is helping alot - cheers

just a query, since 0x is written as the thrid term does that mean the polynomial can be written as simply as 2x³ - 9x² + 15 (i.e. take out the 0x since it = 0 anyway)

P.S I do understand the fact that for purposes of division the 0x needs to be in there - cool, it makes sense yay!

 

[selablad]

Well, it doesn't have to be there I guess. It just makes them all line up better, and makes it more systematic for me? I tried it without but I got confused If you can do it without the 0x then maybe that's better?

 

[bored of sc]

Well, it doesn't have to be there I guess. It just makes them all line up better, and makes it more systematic for me? I tried it without but I got confused If you can do it without the 0x then maybe that's better?

nah, I'm the same as you - it lines up cool and I don't why but it just makes sense when I subtract 0 (even though nothing changes I like reaffirming the fact you are subtracting 0 because its 0xⁿ (I am crazy, lol)

but, thanks - I think it's 'clicked' now