Samuel and Ariana are competing in a speed round for an open position on the math team. To win the spot , each student must factor the same polynomial expression , 12xy * z ^ 2 + 16x ^ 2 * y ^ 2 * z - 32x ^ 2 * y * z , by finding the GCF .

I'm not completely sure but...I believe Samuel factored out a 2 when he should have factored out a 4.

Step-by-step explanation:

First:

You have to factor the equation...

12xyz^2+(162)(y2)z−32x^2yz

     =−32x^2yz+12xyz^2+256y^2z

          =4yz(−8x^2+3xz+64y)

He factor 2 instead of 4

Step-by-step explanation:

4xyz (3z + 4xy - 8x)

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: