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How to Solve Decimal Polynomials

For those who are not math people, the phrase "decimal polynomials" sounds like a foreign language. Yet the process for solving them is exactly the same as the step-by-step process used for solving integer polynomials, only with additional concerns such as decimal alignment. Even when using a calculator this can be tricky but, like all things in math once you know the rules, with concentration and enough practice, it can be mastered.

Instructions

  1. Adding and Subtracting

    • 1

      Scan the problem to make sure they have like terms. (4.4x^2 + 4y - 6.798) + (4.32x - 2.25) cannot be solved since no terms have the same coefficients. (4.4x^2 + 4x) + (4.32x^2 - 2.25) can be solved, however, since you can work with the x^2s.

    • 2

      Add or subtract like terms. Adding the like x^2s in (4.4x^2 + 4x) + (4.32x^2 - 2.25) would be 4.4x^2 + 4.32x^2 = 4.72x^2. Don't forget to line up your decimals.

    • 3

      Drag down the remaining numbers. The final answer for (4.4x^2 + 4x) + (4.32x^2 - 2.25) is 4.72x^2 + 4x - 2.25.

    Multiplying

    • 4

      Multiply decimal polynomials using the FOIL (first, outside, inside, last) method. For example, in (2.56x - .9)(-5.78x - 4.9), you would start by multiplying together the first terms in each polynomial, in this case 2.56x and -5.87x rounded to two decimal places equals -15.03x^2.

    • 5

      Multiply the inside terms. .9 X -5.78x = -5.2x.

    • 6

      Multiply the last terms. -.9 X -4.9 = 44.1

    • 7

      Use the rules of adding and subtracting polynomials to combine any answers from each step with like coefficients. Out of -15.03x^2, -12.54x, -52.x and 44.1, -12.54x and -52x share the same coefficient, x, so they should be added to get -64.54x.

    • 8

      Combine all terms to get a new polynomial. -15.03x^2 - 64.54x + 44.1.

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