Polynomial Equation Word Problems (Mixed Operations)

These lessons help Algebra students learn how to write and solve polynomial equations for algebra word problems.

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How To Solve Polynomial Equation Word Problem?

A tree is supported by a wire anchored in the ground 5 feet from its base. The wire is 1 foot longer than the height that it reaches on the tree. Find the length of the wire.

Polynomial Equation Word Problem

A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air as follows:
h = -16t2 + 8t + 8
a) How long will it take the gymnast to reach the ground?
b) When will the gymnast be 8 feet above the ground?

How To Solve Word Problems With Polynomial Equations?


  1. The sum of a number and its square is 72. Find the number.
  2. The area of a triangle is 44m2. Find the lengths of the legs if one of the legs is 3m longer than the other leg.
  3. The top of a 15-foot ladder is 3 feet farther up a wall than the foo is from the bottom of the wall. How far is the ladder from the bottom of the wall?
  4. A projectile is launched upward from ground level with an initial speed of 98m/s. How high will it go? When will it return to the ground?

How To Write Polynomials For Word Problems?

Learn to write a polynomial for Word problems involving perimeter and area of rectangles and circles.

Learn How To Write And Solve Polynomial Equations

Learn to write and solve polynomial equations for special integers, consecutive integers.

Example 1: Find a number that is 56 less than its square. Let n be the number.
Example 2: Find two consecutive odd integers whose sum is 130.

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