Rational Zeroes Theorem: A slice 1 unit in width is removed from one side of a cube.

[rickyulover76]

I am struggling with my homework that involves Rational Zeroes Theorem. Any assistance with these two questions would be extremely helpful...

Question 1) A slice of 1 unit thickness is removed from one side of a cube. Use the rational zeroes theorem and synthetic division to find the original dimensions of the cube, if the remaining volume is 48 cm^3

My progress: v=x^3
v=x*x*x
v=(x-1)*x*x
48= (x-1)*x*x

Question 2) Use the rational zeroes theorem and synthetic division to find the dimensions of the box if it must have a volume of 150 in^3

My progress:
V=LWH
X=Width
2x= Length
x-2=Height

Thank you very much!

 

[stapel]

Question 1) A slice of 1 unit thickness is removed from one side of a cube. Use the rational zeroes theorem and synthetic division to find the original dimensions of the cube, if the remaining volume is 48 cm^3

My progress: v=x^3
v=x*x*x
v=(x-1)*x*x
48= (x-1)*x*x

It might be helpful to label things a bit more clearly:

. . .original linear dimensions: x

. . .original volume: x*x*x = x^3

. . .one dimension is shortened: x - 1

. . .new volume: (x - 1)*x*x = x^3 - x^2

. . .remaining volume: 48 = x^3 - x^2

What "=0" polynomial can you obtain from the last equation above? (They gave you that info here.) Applying the Rational Zeroes Theorem, what possible zeroes can you find? What do you get when you plug these, and the polynomial from the equation you found, into synthetic division? (They gave you that info here.)

Question 2) Use the rational zeroes theorem and synthetic division to find the dimensions of the box if it must have a volume of 150 in^3

I don't understand the use of "the" in "the box". Are they referring to the same box here, so they're talking about the "remaining" volume? But then the "a" in "a volume" doesn't make sense... :shock:

My progress:
V=LWH
X=Width
2x= Length
x-2=Height

Thank you very much!

How did you obtain your expressions for "Length" and "Height"? (And how does "X" relate to "x"?) Was there maybe a picture that went with this exercise? Thank you!