Question

simplify \(\Large \dfrac{4x^3-2x^2+8x+8}{2x+1}\)

Answer 1

well you can see that you have a common denominator so you can devide 2 on the top.
Ex. \[2x^3 - x^2 + 4x + 4/x+ 1\] then
Ex.2 \[(2x^3 - x^2) + (4x + 4) = x^2(2x - 1) + 4(x + 1)\]
so you get left with \[(x^2 + 4)(2x - 1)\] because (x + 1) cancels out

Answer 2

ok

Answer 3

are you ok

Answer 4

yes im fine y u ask

Answer 5

just making sure

Answer 6

ok so do we divide all the x values by the constant and the variables

Answer 7

if we run a synthetic division, x = -1/2


4x^3 -2x^2 +8x +8
0 -2 -2 -3
-----------------------
-1/2 ) 4 -4 6 R=5

Answer 8

FriedRice, your solution is not correct. There is no common factor between the numerator and denominator. While you can factor 2 out of the numerator, factoring 2 out of the denominator would yield a denominator of \[x+\frac{ 1 }{ 2 }\]

Answer 9

4x^2 -4x+6 + 5/(2x+1)

Answer 10

If you perform long division, you end up with \[2x^2-2x+5+\frac{ 3 }{ 2x+1 }\]. As you can see, there is a remainder.

Answer 11

ok

Answer 12

lol, yeah, mine a little off .... -4*-1/2 = 2, not -2

Answer 13

4x^3 -2x^2 +8x +8
0 -2 2 -5
-----------------------
-1/2 ) 4 -4 10 R=3

thats better

Answer 14

What course is this for, jazzyfa30? It would help for us to know what context the instruction "simply" is being used in.

Answer 15

algebra 2

Answer 16

Are you working on polynomial long division, or do you believe this was supposed to be a neatly factored solution? As you can see, there is no "neat" solution to this beyond the long division I performed above.

Answer 17

polynomial

Answer 18

if you flip the polys you can create a power series representation :)

Answer 19

If long division of polynomials is where you are at in your course, then the quotient + remainder above would be the solution. If you were expected to factor and then simplify by canceling factors, this won't work in this case, as the polynomial in the numerator cannot be factored over integers. Thus, in that case, I would say 'this can't be simplified.'

Answer 20

lol @ power series representation -- that'd be fun, right?

Answer 21

8 -8x +14x^2-24x^3+48x^4 - ....
---------------------
1+2x ) 8 +8x -2x^2 +4x^3
-8-16x
-------
-8x -2x^2
8x +16x^2
-----------
14x^2 +4x^3
-14x^2 -28x^3
---------------
-24x^3
24x^3 +48x^4
--------------
then it evens out

Answer 22

thank u for stepping in and ir was a r=3 thingy at the top i wish i could the both of you a medal i am going to open 2 more questions and give you guys a medal Thank you @amistre and @ssilvestro

Answer 23

^ @amistre64

Answer 24

youre welcome ;)

Answer 25

Thank you!