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All courses Algebra II · A-CED.1 15 of 55
Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.

Write and solve a polynomial equation from a context

Problem
Write \(x(x~+~2)(x~+~3)~=~60\) in zero form and find its positive solution to the nearest thousandth.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Move everything to one side so the volume equation becomes a polynomial equation equal to \(0\).

A box dimension must be positive, so after solving the polynomial equation you keep only the positive root that fits the context.

Solution walkthrough

01

Translate the product condition

\[x(x+2)(x+3)=60\]

The three factors are the given quantities, and their product is required to equal 60.

02

Write zero form

\[x(x+2)(x+3)-60=0\]

Subtracting 60 places every term on one side, producing the requested equation in zero form.

03

Locate the positive root

\[f(2.461)~\text{approx}~-0.046;~f(2.462)~\text{approx}~0.002\]

For f(x)=x(x+2)(x+3)-60, the sign change brackets a positive zero between 2.461 and 2.462. A numerical solve gives about 2.46195, which rounds to 2.462 to the nearest thousandth.

04

State and check the requested solution

\[x(x+2)(x+3)-60=0;~x~\text{approx}~2.462\]

Substituting the unrounded numerical root makes the product 60, and the requested positive solution rounds to 2.462, choice A.

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Another way

  1. Expand to x³+5x²+6x-60=0 and use a graphing or numerical root solver, then keep only the positive root requested.

!

Common mistake

Do not round an intermediate trial value before locating the root accurately enough. Keep extra digits, then round the final positive solution to three decimal places.

Solution walkthrough video