How to Factor a Third Degree Polynomial

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Functions with factors of two or more are called polynomial functions. These functions have many numbers that can be considered solutions. In fact, most polynomials have infinite solutions. The key to solving polynomials with a factor of three or higher is finding the equation's zeros.

Things You'll Need

  • Graphing calculator or graph paper
  • Enter the function into your graphing calculator to determine the zeros. Zeros are points on the graph where the function's lines cross either the x or y axis. For example, in the function f(x)= x^3 + 2x^2 - x - 2, the zeros are 1, -1 and -2.

  • Solve for the numbers where your lines intersect the graph lines. In the example, you would be solving for f(1), f(-1) and f(2). When all of these are solved, the answer becomes zero.

  • Check your answers by factoring the equation to its simplest form. This will allow you to see why you got the answers you did. In the example, the problem factors to ( x - 1 ) ( x + 1 ) ( x - 2 ).

References

  • Photo Credit Jupiterimages/Goodshoot/Getty Images
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