Me

x y
1 12
5 40
10 50
15 170
20 280
25 410

what is the curve of best fit for the data shown?
a) y = 16x2 - 51x + 9
b) y = 0.2x2 + x + 23
c) y = 10x2 - 0.5x + 8
d) y = 0.6x2 - 0.02x + 11

assuming all factors are real, factor x4 + y4.
a) (x + y)(x + y)(x - y)
b) (x2 + y2)(x + y)(x - y)
c) (x2 + y2)(x - y)(x - y)
d) cannot be factored in the real number system

The best fit curve for #1 is D. The easiest way to check these is by pluggin in to the equation and seeing if they come close. By doing just the first ordered pair along, it is apparent that only D will work.

With x = 1 input

A) -36

B) 24.2

C) 17.5

D) 11.58

#2 is also D. We can tell this because multiplying any of these options always results in a middle term between them. For instance, if you multiply out C, you will not only get x^4 and x^4, but you will also get terms such as 4x^2y^2 in the middle.