Mady has an infinite number of balls and empty boxes available to her. the empty boxes, each capable of holding four balls, are arranged in a row from left to right. at the first step, she places a ball in the first box of the row. at each subsequent step, she places a ball in the first box of the row that still has room for a ball and empties any previous boxes. how many balls in total are in the boxes as a result of mady's $2010$th step?

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.