2.3: Polynomial Equations - Period 3/4

Polynomial Equations
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.

We end up with the result 9x^2 + 96x + 633 with 0 remainders.
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.