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?

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