A box has a volume given by the trinomial 2x^3-16x^2-40x. What are the possible dimensions of the box? Use factoring.
To find the possible dimensions of the box, we need to factor the given trinomial:
2x^3 - 16x^2 - 40x = 2x(x^2 - 8x - 20) = 2x(x - 10)(x + 2)
So the possible dimensions of the box are:
- Length = x - 10
- Width = x + 2
- Height = 2x
Note that x must be positive for the dimensions to make sense in the context of a box.
To find the possible dimensions of the box, we need to factor the given trinomial.
The trinomial is: 2x^3 - 16x^2 - 40x
First, we can factor out the greatest common factor (GCF) of the terms, which is 2x:
2x(x^2 - 8x - 20)
Next, we need to factor the quadratic expression inside the parentheses, x^2 - 8x - 20.
To do this, we need to find two numbers whose product is equal to the product of the coefficient of x^2 (1) and the constant term (-20), and whose sum is equal to the coefficient of x (-8).
The two numbers that satisfy these conditions are -10 and 2.
Therefore, the expression can be factored as:
2x(x - 10)(x + 2)
This means that the possible dimensions of the box are x, x - 10, and x + 2.