The volume of a rectangular box is (x^3+6x^2+11x+6) cm^3. The box is (x+3) cm long and (x+2) cm wide . How high is the box
To find the height of the box, we need to divide the volume of the box by the product of its length and width. Let's break down the process step by step:
1. First, let's identify the given information:
- Volume of the box: x^3 + 6x^2 + 11x + 6 cm^3
- Length of the box: x + 3 cm
- Width of the box: x + 2 cm
2. Now, let's express the volume of the box as a mathematical expression using the length, width, and height:
Volume = Length × Width × Height
x^3 + 6x^2 + 11x + 6 = (x + 3)(x + 2) × Height
3. To find the height, we need to divide both sides of the equation by (x + 3)(x + 2):
(x^3 + 6x^2 + 11x + 6) / [(x + 3)(x + 2)] = Height
4. Simplify the expression on the right side by canceling out common factors:
(x^3 + 6x^2 + 11x + 6) / [(x + 3)(x + 2)] = Height
(x^3 + 6x^2 + 11x + 6) / (x^2 + 5x + 6) = Height
5. Now, we have the height of the box in terms of 'x' as:
Height = (x^3 + 6x^2 + 11x + 6) / (x^2 + 5x + 6) cm
Thus, the height of the box is given by the expression (x^3 + 6x^2 + 11x + 6) / (x^2 + 5x + 6) cm.