Hello, Andrew!
1) Sketch the graph of: .$\displaystyle y \:=\:4x^3  8x^211x3$
I tried it and got: .$\displaystyle (x3)(4x^2+4x+1)$ . . . . Good!
I can't factorise the quadratic. . . . . you can't? The function is a "positive cubic"
. . It rises to the right and falls to the left.
It factors to: .$\displaystyle y \:=\:(x3)(2x+1)^2$
The xintercepts are: .$\displaystyle 3\text{ and }\frac{1}{2}$
Since the intercept $\displaystyle x = \frac{1}{2}$ has multiplicity 2,
. . the graph is tangent to the xaxis there.
Code:

 *

½  *
   * +    *  
* * * 3
*  *

* 

$\displaystyle 2)\;\;\left(\frac{3w}{2}  \frac{5}{4w}\right)^3 $
Instructions?
. . Are we supposed to expand and simplify it?