Help please!

#1. x^4-52x^2+576 = 0
Easy enough to check. They even give you the values to try. Just do a few synthetic divisions to see whether the proposed values work. Synthetic division is fast and easy. Once you have found two roots, you end up with a quadratic, and that's no trouble.
However, I'd try C first, since you can just divide by x^2-16 or x^2-36 to check it.
Or, if you let u = x^2, you have a quadratic in u:
u^2 - 52u + 576 = (u-16)(u-36)
That means the factors are (x^2-16)(x^2-36)

#2. x^3 = 216 = 6^3
So, you know the real root is 6
The complex roots are 6cis(2π/3) and 6cis(4π/3)
or, 6(1±i√3)/2

#3. More of the same. You want to solve
x(x+5)(3x-1) = 7.6*1728
3x^3+14x^2-5x = 13132.8
3x^3 + 14x^2 - 5x - 13133 = 0
Now, you can go through the motions of trying to solve this, but a few seconds with your calculator shows that A gives a volume of 13200, which is pretty close. C and D are obviously wrong, since the dimensions do not fit the requirements.