38.4k views
3 votes
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?

2 Answers

2 votes

Answer:

116

Explanation:

User Bachposer
by
8.2k points
4 votes
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

User RChugunov
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.