Today we quickly learned how to turn polynomial functions into polynomial equations. Using the example from the class, V(x) = 9x^3 + 60x^2 + 249x with the given volume of 2532 cm^3, we find the maximum thickness of a block of ice.
First, we set up the equation:
V = 2532
V(x) = 9x^3 + 60x^2 + 249x
2532 = 9x^3 + 60x^2 + 249x
0 = 9x^3 + 60x^2 + 249x - 2532
Next, we use the factor theorem to determine if there are any integral roots:
- we fine that f(4) = 0
- we use either synthetic division or long division.
0 = (x-4)(9x^2 + 96x + 633)
Since it is not a real root it is, therefore, the max thickness the block can be is 4 cm.
Comment if there are any errors within the post.