Question

1. the volume of a refrigerator is described by the function ( v(x) = x^3 - 3x^2 - 16x - 12 ). the height of the refrigerator is ( x + 2 ). what are the other two dimensions?

a. ( x - 2 ) and ( x + 3 )
b. ( x + 6 ) and ( x - 1 )
c. ( x - 3 ) and ( x + 2 )
d. ( x - 6 ) and ( x + 1 )

Explanation:

Step1: Divide volume by height

We perform polynomial long division of $V(x) = x^3 - 3x^2 - 16x - 12$ by the height $(x+2)$ to find the product of the other two dimensions.
$$\frac{x^3 - 3x^2 - 16x - 12}{x+2} = x^2 - 5x - 6$$

Step2: Factor the quadratic result

Factor the quadratic polynomial $x^2 - 5x - 6$ to get the two missing dimensions.
$$x^2 - 5x - 6 = (x-6)(x+1)$$

Answer:

D. $x - 6$ and $x + 1$