anonymous
  • anonymous
If we divide the polynomial x4 + 4x3 + 2x2 + x + 4 by x2 + 3x, what will be the remainder
Mathematics
schrodinger
  • schrodinger
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UsukiDoll
  • UsukiDoll
\[x^4+4x^3+2x^2+x+4\] by \[x^2+3x\] have you made any attempts to this problem?
anonymous
  • anonymous
x4+4x3+2x2+x+4byx2+3x =x4+4x3+2x2+x+4bx2y+3x Combine Like Terms: =x4+4x3+2x2+x+4bx2y+3x =(4bx2y)+(x4)+(4x3)+(2x2)+(x+3x) =4bx2y+x4+4x3+2x2+4x Answer: =4bx2y+x4+4x3+2x2+4x right?
UsukiDoll
  • UsukiDoll
whoa man.. direct answers are against openstudy's code of conduct

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UsukiDoll
  • UsukiDoll
and this is long division... I'm not doing that until the official poster responds
anonymous
  • anonymous
i have made attempts and none of the answer are there
UsukiDoll
  • UsukiDoll
so you had tried the long division method to this problem?
anonymous
  • anonymous
thats not a direct answer i said it step by step and just to let you know i did this on the other post and they said that they under stood it completely now
anonymous
  • anonymous
yes sir i have. would you like to see the answer choices
UsukiDoll
  • UsukiDoll
yeah I like to see the choices
anonymous
  • anonymous
A) x2 + 3x B) 4x + 4 C) x2 + x – 2 D) 4 E) 0 That is all of the answer choices
UsukiDoll
  • UsukiDoll
ok... so this problem is asking to divide... so we need long division. |dw:1435149580706:dw|
UsukiDoll
  • UsukiDoll
wow.. this is long.. so first of all we need to get rid of the x^4
anonymous
  • anonymous
yea it sucks i'm in Algebra 2.
UsukiDoll
  • UsukiDoll
I've learned this in Algebra 1 O_O anyway , are you aware of the exponential rules?
anonymous
  • anonymous
Don't you combine them? If its not that then I don't know about it
UsukiDoll
  • UsukiDoll
one of the exponential rules is \[n^{a+b}=n^{a}n^{b}\] let n = x and a = 2 \[x^{2+b}\] what does b need to equal in order to get \[x^4 \]?
anonymous
  • anonymous
2 if i'm not mistaking
UsukiDoll
  • UsukiDoll
yes because \[x^{2+2} =x^2x^2\]
UsukiDoll
  • UsukiDoll
so we need an x^2
UsukiDoll
  • UsukiDoll
|dw:1435149984739:dw|
anonymous
  • anonymous
Okay. Inside of the sqrt there is a 2x^2
UsukiDoll
  • UsukiDoll
we have to go slowly.. getting rid of the x^4 and x^3 is a great idea at this point
anonymous
  • anonymous
Alright so would we divide x^2+3x to x^4
UsukiDoll
  • UsukiDoll
we need to multiply (x^2+3x) by x^2
UsukiDoll
  • UsukiDoll
|dw:1435150150946:dw|
anonymous
  • anonymous
Okay so its going to be x^4+3x^3
UsukiDoll
  • UsukiDoll
yeah...one problem we need to switch the signs.
UsukiDoll
  • UsukiDoll
then we can use addition.
UsukiDoll
  • UsukiDoll
let's just distribute the - -(x^4+3x^3) = -x^4-3x^3
UsukiDoll
  • UsukiDoll
|dw:1435150318360:dw|
UsukiDoll
  • UsukiDoll
oh the plus sign is invisible for long division. I'll just put it in () |dw:1435150362975:dw|
UsukiDoll
  • UsukiDoll
so what's x^4-x^4 and what's 4x^3-3x^3 ?
anonymous
  • anonymous
Okay so if we are trying to change the sign wouldn't it be x^8 and x^6
UsukiDoll
  • UsukiDoll
whoa no...
UsukiDoll
  • UsukiDoll
you only use the exponent rule to figure out what's missing. Like what I did earlier. with the x^4 = x^{2+b}
anonymous
  • anonymous
ok. sorry im not much of a math person. I love history
anonymous
  • anonymous
Oh Okay.
UsukiDoll
  • UsukiDoll
|dw:1435150555870:dw| let's try this again what's x^4-x^4 and 4x^3-3x^3 ?
anonymous
  • anonymous
x and x. right.
anonymous
  • anonymous
If we divide the polynomial x4 + 4x3 + 2x2 + x + 4 by x2 + 3x, what will be the remainder? Here is the full question
UsukiDoll
  • UsukiDoll
...... let's make it easier I'm going to factor out the x^3 x^3(4-3)
UsukiDoll
  • UsukiDoll
well we need to do long division...this is the right method
UsukiDoll
  • UsukiDoll
or synthetic division which is faster but I forgot
UsukiDoll
  • UsukiDoll
x^4(1-1) x^3(4-3) try solving those two ^
anonymous
  • anonymous
You forgot how to do synthetic division
UsukiDoll
  • UsukiDoll
I've practiced more with long division...it stuck in my head.
anonymous
  • anonymous
Oh okay, and i got x^4-x^4 and 4x^3-3x^3
UsukiDoll
  • UsukiDoll
wow @_@!
UsukiDoll
  • UsukiDoll
try again... x^4-x^4 is the same as x^4(1-1) what's 1-1 ?
anonymous
  • anonymous
sorry i suck at math.
anonymous
  • anonymous
1-1=0
UsukiDoll
  • UsukiDoll
yes and what's x^4(0) also known as what's x^4 multiplied by 0
anonymous
  • anonymous
0
anonymous
  • anonymous
cause anything that is multiplyed by 0 is 0
UsukiDoll
  • UsukiDoll
yes! so the x^4's are gone! SImilarly what's x^3(4-3) ? what;s 4-3?!
UsukiDoll
  • UsukiDoll
what's 4-3?
anonymous
  • anonymous
1
UsukiDoll
  • UsukiDoll
yes and x^3 times 1 is?
anonymous
  • anonymous
x^3
UsukiDoll
  • UsukiDoll
yay!
anonymous
  • anonymous
lol im getting it slowly but surely
UsukiDoll
  • UsukiDoll
|dw:1435151077510:dw| so after we solve that we bring the rest of the terms down
UsukiDoll
  • UsukiDoll
now our new goal is to get rid of the x^3
UsukiDoll
  • UsukiDoll
remember the exponent rule?
anonymous
  • anonymous
na+b=nanb let n = x and a = 2 x2+b what does b need to equal in order to get x4 that one
UsukiDoll
  • UsukiDoll
\[x^{2+b} =x^2x^b\]
UsukiDoll
  • UsukiDoll
yup now what value of b is needed to produce x^3?
anonymous
  • anonymous
1
UsukiDoll
  • UsukiDoll
yes.
anonymous
  • anonymous
ok so it would be x^3-x^3
anonymous
  • anonymous
which would get rid of each other
UsukiDoll
  • UsukiDoll
|dw:1435151215690:dw|
UsukiDoll
  • UsukiDoll
now this time x(x^2+3x) and switch signs after distributing
anonymous
  • anonymous
ok so it is 4x^3
UsukiDoll
  • UsukiDoll
|dw:1435151316916:dw|
UsukiDoll
  • UsukiDoll
?!?!?!! |dw:1435151357797:dw|
anonymous
  • anonymous
my bad. x^3-3x^2 Right.
UsukiDoll
  • UsukiDoll
something is off.. are you sure the x^2 part of your original question is correct?
anonymous
  • anonymous
yes it is ill post the whole question in here
anonymous
  • anonymous
If we divide the polynomial x4 + 4x3 + 2x2 + x + 4 by x2 + 3x, what will be the remainder?
UsukiDoll
  • UsukiDoll
let's try continuing and see what happens..
anonymous
  • anonymous
Alright
UsukiDoll
  • UsukiDoll
|dw:1435151602784:dw|
anonymous
  • anonymous
so the x^3 would cancel and it would be -x^2
UsukiDoll
  • UsukiDoll
I see the question is asking for the remainder XD. we're not done xD we're doing it right heheeh so what's x^3-x^3 and 2x^2-3x^2 ... yes x^3 is gone and we will have -x^2
anonymous
  • anonymous
so i did that part right
UsukiDoll
  • UsukiDoll
|dw:1435151714443:dw|
UsukiDoll
  • UsukiDoll
the last part is a digit, but it has to be negative
UsukiDoll
  • UsukiDoll
because when switching the sign it will be positive.. and I have a negative -x^2 right at me
anonymous
  • anonymous
what do yo mean by that
UsukiDoll
  • UsukiDoll
we've reached the end of the problem.. after all the exponents are used up, it's down to digits. like 1 2 3 4 ...
UsukiDoll
  • UsukiDoll
there can only be 1 that will produce x^2
anonymous
  • anonymous
ok so the only one that can be right is 4 then. cause i have 0 and 4 as a answer
UsukiDoll
  • UsukiDoll
0 is no remainder.. I doubt that will happen
anonymous
  • anonymous
A) x2 + 3x B) 4x + 4 C) x2 + x – 2 D) 4 E) 0 Those are the answer
UsukiDoll
  • UsukiDoll
|dw:1435151939146:dw|
UsukiDoll
  • UsukiDoll
it's not going to be 0 . trust me.. I did the final step in my head.
UsukiDoll
  • UsukiDoll
quick question what's -1(x^2) ?
anonymous
  • anonymous
-x^2 right
UsukiDoll
  • UsukiDoll
yeah.. noticed that I needed the -1 to produce the -x^2-3x but I need to switch signs because we already have a -x^2 present!
anonymous
  • anonymous
ok so it becomes positive
UsukiDoll
  • UsukiDoll
|dw:1435152046028:dw|
UsukiDoll
  • UsukiDoll
yup you just need to compute x+3x and 4+0 that's your remainder
anonymous
  • anonymous
SO it would be 4
UsukiDoll
  • UsukiDoll
oh I saw what happened I confused regular division with polynomial division. In polynomial division we can have bigger or smaller than the original numbers... can't have that in regular division xD (that was for the x^2 remark) you're missing x+3x!!!!!!!!
UsukiDoll
  • UsukiDoll
x(1+3) what's 1+3 ?
anonymous
  • anonymous
4
UsukiDoll
  • UsukiDoll
yeah and 4(x) is ?
anonymous
  • anonymous
4x
UsukiDoll
  • UsukiDoll
yeah with 4x and 4 combined together we have 4+4x
UsukiDoll
  • UsukiDoll
|dw:1435152315128:dw|
anonymous
  • anonymous
Ok so thats the remainder
UsukiDoll
  • UsukiDoll
anything left over on the bottom is the remainder.. what aloud did was way off.
UsukiDoll
  • UsukiDoll
so that's done... yay x)

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