Skip to main content

Topic

Word problems of polynomials

My Progress

Pug Score

0%

Study Points

+0

Unlock Full Access
Adaptive practice
Video lessons

Read

Polynomial Word Problems

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.

Turning words into a polynomial A box word problem: height is x, length is 3 more than x, and width is 2 less than x. The volume, length times width times height, becomes a polynomial in x. height = x, length = x+3, width = x−2 V = x(x+3)(x−2) = x³ + x² − 6x
Height x, length x+3, width x−2: the volume becomes the polynomial x³+x²−6x.

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.

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.

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.

Related lessons