Help with a problem please? ^.^?

Question

(4t^3-5t-1)/2t-1
My fathr did it in such a way that wud never understand, and i always come out with a wrong answer whn i do it myself.
So can some one please explain this to me? Thank u! @_@

By the way, Merry Christmas and Happy Holidays! ^-^

By the way, excuse my spelling, i was in a bit of a rush

Oh sorry, yes i have to simplify it

Answer 1

Hi,

Merry Christmas!!

........._2t²_________
2t - 1)4t³.+.0t².-.5t.-.1
..........4t³.-.2t² <= change signs and add
.........-----------

........._2t².+.t________
2t - 1)4t³.+.0t².-.5t.-.1
.........-4t³.+.2t²
.........-----------
..................2t².-.5t
..................2t².-...t <= change signs and add
.................----------


........._2t².+.t_.-_2______
2t - 1)4t³.+.0t².-.5t.-.1
.........-4t³.+.2t²
.........-----------
..................2t².-.5t
.................-2t².+..t
.................----------
........................-4t.-1
........................-4t.+2 <= change signs and add
---------------------------

........._2t².+.t_.-_2______
2t - 1)4t³.+.0t².-.5t.-.1
.........-4t³.+.2t²
.........-----------
..................2t².-.5t
.................-2t².+..t
.................----------
........................-4t.-1
.........................4t.-2
---------------------------
With remainder of -3

Answer: 2t² + t - 2 -3/(2t - 1)

I hope that helps!! Merry Christmas!! :-)
_/\_
\..../
/.^.\

Answer 2

First, I'm assuming you mean (4t^3-5t-1)/(2t-1). The way you have it written, the 1 is not part of the denominator.

Next, I'm not exactly sure what you're trying to do. Are you just trying to simplify it using division? Or are you trying to do something else, like find asymptotes? I ask because it doesn't divide evenly, so dividing doesn't really make it any simpler.

Answer 3

The cubic on top can be factored by simple inspection. If t = -1, the cubic = 0, so one of the factors is (t + 1)

You then have :

[(t + 1)(4t² - 4t - 1)] / (2t - 1)

I can't simplify it further.

You can divide, but there is always a remainder.

Answer 4

(4t^2 - 5t - 1)/(2t - 1)

Hopefully you meant the exponent in the first term to be 2

Factor the trinomial to see if one of its factors is equal to (2t - 1) so you can cancel them both

Unfortunately, the trinomial does not factor easily

The problem is in its simplest form or you have typed it wrong

Answer 5

What exactly is the goal of the problem? Simplification? Polynomial long division? Sorry to seem unhelpful, but I'm not to clear on what you need to do.

Answer 6

1t