The volume V (in cubic feet) of a rectangular room can be modeled by V(x)= 2x^3-14x^2+12x, where x is the length (in feet) if the room. Factor the function. Use your factorization to determined the values of x for which the model makes sense

The values of x for which the model makes sense is .

Step-by-step explanation:

From statement we have the following expression for the volume of the rectangular room is:

(1)

Where:

- Volume of the rectangular room, measured in cubic feet.

- Length of the room, measured in feet.

By Algebraic means we factorize the polynomial:

Given that both volume and length must be positive variables, then the following conditions must be satisfied:

Then, the values of x for which the model makes sense is .

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.