Math

3x^3-9x^2-31x+5=0

How do I find the zeros, using synthetic division

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  1. let f(x) = 3x^3-9x^2-31x+5
    f(1) = 3 - 9 - 31 + 5 ≠ 0
    f(-1) ≠ 0
    f(5) = 375 - 225 - 155 + 5 = 0
    so x = 5 , and x-5 is a factor

    I assume you know how to perform synthetic division.

    You should get (x-5)(3x^2 + 6x - 1)

    This quadratic produces two more zeros, use the quadratic formula to find them

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  2. There is a nice online calculator at

    https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

    It will show the steps involved.

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