Long division with polynomial's help?

Question

(4X^3-2X^2+8X-8) divided by (2X+1)

Answer 1

2x^2-2x+5
(2x+1) 4x^3-2x^2+8x-8
4x^3+2x^2
-4x^2+8x
-4x^2-2x
10x-8
10x+5
-13
use b^2-4ac<0 to prove there is no real value to the expression 2x^2-2x+5

but there are 2 imaginory values
use the equation -b+or- root(b^2-4ac)/2a to fid these values

2 values are -2+or-root(-36)/4

-0.5+1.5i(imaginory value) and -0.5-1.5i(imaginory)

if u want the answer in real parts

its 2x^2-2x+5-(13/2x+1)

Answer 2

Don't be fooled by apparent complexity. Write this one out and you'll see for yourself:
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(2x + 1) |((4X^3-2X^2+8X-8))

Notice first that you have to multiply the '2x+1' part by 2X^2 just to get the first part of the polynomial correct (i.e., 2x^2*(2x+1) = 4x^3+2x^2)

Subtract that from the '(4X^3-2X^2+8X-8)' part and you're left with

_______
(2x+1) |(8x - 8

Then, multiply the '2x+1' part by 4, and subtract that result from the '8x-8' part...

you end up with: 2x^2 + 4 - 4/(2x+1)

Answer 3

well with this you can devide both the parts by 2 and use synthetic division
so you now have 2x^3-x^2+4x-4 devided by x+1/2

-1/2| 2 -1 4 -4
...........-1 1 -5/2
........2 -2 5 -13/2

2x^2 -2x+5 - 13/(2x+1)

Answer 4

(4X^3-2X^2+8X-8)/(2x+1)
2x^2 + n | (4X^3-2X^2+8X-8 - 4X^3 - 2X^2)
2x^2 + n | (-4X^2+8X-8)
2x^2 - 2x + n | (-4X^2+8X-8 + 4x^2 + 4x)
2x^2 - 2x + n | (12X-8)
2x^2 - 2x + 6 + n | (12X-8 -12x - 6)
2x^2 - 2x + 6 + n | (-14)
2x^2 - 2x + 6 - (14/2x+1)

Answer 5

-8 + 8X + -2X2 + 4X3 / 1 + 2X