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A box has a volume given by the trinomial x^3 5x^2 -24x What are the possible dimensions of the box?

Given the volume, how to find the dimensions?

Verified Answer :

apologiabiology

volume is legnth times width times height so 3 dimentions
thee teacher probabl y wants you to factor the trinomial into 3 factors so
x^3+5x^2-24x
first factor out x
x(x^2+5x-24)
then factor
find what 2 numbers multiply to get -24 and add to get 5
the numbers are -3 and 8
x^2+5x-24 factors to
(x-3)(x+8)
the factored form is
(x)(x-3)(x+8)=volume
no dimention can be ≤0 so therefor
x≤0

x-3≤0
add 3
x≤3

x+8≤0
subtract 8
x≤-8

so the values for x is x<3


so if you had the volume, let's say 42 then
x^3+5x^2-24x=42
subtract 42 from both sides
x^3+5x^2-24x-42=0
factor and set each to zero to find the dimentions

Answer:

116

Step-by-step explanation: