Polynomial (Fish Tank Problem)

The problem says "Ryan has a cubic fish tank with a volume of x(3rd power) inches. He wants to buy more fish, which requires him to upgrade to a larger fish tank. The new tank has the same height, but length and width are each increased by a whole number of inches. If the volume of the new tank is x(3rd power) + 11x(2nd power) + 28x inches, then how much was each increase?


I have no clue how to even go about doing this.

Here's what I'd so.

Think of each polynomial as any number. If Ryan started out with a fish tank with a volume of 3 inches and went to one with a volume of 20 inches then what would be increase? 17. So the new tank is the different of the new one and the previous one.

So we have:\(\displaystyle \L \;(x^3\,+\,11x^2\,+\,28x)\,-\,(x^3)\)

Solving that you get \(\displaystyle \;11x^2\,+\,28x\,\)or\(\displaystyle \,x(11x\,+\,28)\,\)inches.

let L = length increase
W = width increase
x = same old height

new volume = x(x+L)(x+W) =
x[x² + (W+L)x + LW] =
x³ + (W+L)x² + LWx

the last expression is equal to the new tank volume ...

x³ + 11x² + 28x

equating coefficients ... W+L = 11 and LW = 28

what are two numbers whose sum is 11 and whose product is 28 ?