Frank’ s Tank Frank won a magic goldfish at Math Fiesta last year. His goldfish was small, so he bought a cube-shaped fish tank with a volume of 1 ft3.

Frank’s goldfish grows every year, so every year he buys a tank that is one foot longer, wider, and taller than the year before. If Frank’s buys a new tank for 6 years, what will the dimensions of the 6th tank be?

Fill out the table below to find the appropriate dimensions.

um 1x bigger and dimensional

Step-by-step explanation:

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.