A perfect rectangular prism is carved from a solid block of soapstone. It has a length of 12, a width of 10 cm and a height of 6 cm. The carver wants to reduce the volume of the block by 400cm^3 by removing the same amount from all three dimensions. Write a polynomial equation that represents the volume of the block. Calculate algebraically how much the carver should remove from each dimension. V(x)=(12-x)(10-x)(6-x)

Help me, pretty please LOL

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.