A polynomial word problem describes a real situation that must be translated into a polynomial expression or equation, then solved. Learn the four-step process using a box-volume example, and see the common problem types this covers.
Turning words into a polynomial
A polynomial word problem describes a real situation in words, and your job is to translate it into a polynomial expression or equation, then solve it. The hardest part is usually the translation, not the algebra.
Height x, length x+3, width x−2: the volume becomes the polynomial x³+x²−6x.
Worked example: box volume
A box has height x, length 3 more than the height, and width 2 less than the height. Translating: height = x, length = x + 3, width = x − 2. Volume is length × width × height: V = x(x + 3)(x − 2), which expands to x³ + x² − 6x.
Steps for any polynomial word problem
1) Identify the unknown and name it (usually x). 2) Write every other quantity in terms of that unknown. 3) Combine the quantities with the correct operation — multiplication for area or volume, addition for totals. 4) If you're given a target value, set the polynomial equal to it and solve the resulting equation.
Common problem types
Most polynomial word problems involve area, volume, or a total made of several parts, all covered more broadly under applications of polynomials. Whatever the setup, the translation step — naming the unknown and expressing everything else in terms of it — is always the same.