1. ## Algebra HW questions

Hello,

I am currently taking a college algebra class online and needs some help on a few homework questions. My instructor has not gotten back to me yet, so I found this forum and thought I would see if any of you could get me in the right direction.

The first problem is dealing with graphing a quadratic function; plus finding the real zeros and minimums for:

f(x)= (1/2)x^3 - 8x^2 - 3

The next one is to find all the solutions (real and complexe) for:

4x^3 - 4x^2 + 3x - 3 = 0

And, one more using long division: (6x^3 + x^2 - 1) / (x-2)

If anyone could help me out with these I would appreciate it. I have not had an algebra class for a few years and taking the class in an online format has not been the best experience. Thanks if you can help out.

2. Originally Posted by RBry
...

The next one is to find all the solutions (real and complexe) for:

4x^3 - 4x^2 + 3x - 3 = 0

And, one more using long division: (6x^3 + x^2 - 1) / (x-2)

...
You can factor the LHS of the equation:

$\displaystyle 4x^3 - 4x^2 + 3x - 3 = 0~\implies~4x^2(x-1)+3(x-1)=0~\implies~(x-1)(4x^2+3)=0$

I'll leave the rest for you.

Long division:
Code:
                                                           51
(6x^3 +  x^2      -  1) ÷ (x - 2) = 6x^2 + 13x + 26 + ------
-(6x^3 - 12x^2)                                         x - 2
--------------------
13x^2 + 0*x
-(13x^2 - 26x)
----------------
26x - 1
-(26x - 52)
---------------
51