Raymond B. answered • 03/26/23
Tutor
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(2)
Math, microeconomics or criminal justice
6x^3 -3x^2 -45x
= x(6x^2 -3x -45)
= x(3x-9)(2x+5)
height = x
length = 3x-9
height = 2x+5
x= 0, 3, and -5/2 are 3 zeros
if volume = 0, then sides are 0,3, and -2.5 which doesn't make sense in two ways including a negative side
but if v>0 then endless possibilities
but one is when x >3
let x = 4
then
4 by 3 by 13
or another possibility
let x =5
then
5 by 6 by 15
x=6
6 by 9 by 17
x=7
7 by 12 by 19
x=8
8 by 15 by 21
x= 9
9 by 18 by 23
x=10
10 by 21 by 25
...
Mark M.
Also the polynomial is factored as if it were equal to zero. Yet if the polynomial represents the volume it cannot be equal to zero.
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03/26/23
Brenda D.
tutor
I agree with Mark M. above relative to solving for x. I see something else in the problem, it only asks for the expressions for the dimensions. I get from the question that the student was just supposed to factor the expression to get expressions for length, width and height, not try solve for x. That said there can be more than one set of factors such as 3x(x-3)(2x+5) for the expression. Since this was just an expression not an equation, I still wonder if the student was supposed to qualify the factors or restrict the expressions since distances must be positive and volume can’t be 0.
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03/26/23
Mark M.
So a unique solution (what of irrational numbers?) does not exist.03/26/23