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Math Help - Finding Zeros and Linear Factorization

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    Finding Zeros and Linear Factorization

    f(x)=x^3+7x-22 and linear factorization of f(x)
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    Quote Originally Posted by greenpumpkins View Post
    f(x)=x^3+7x-22 and linear factorization of f(x)
    It is interesting that your title puts "finding zeros" first! Of course a typical way of solving a polynomial equation is to first factor it, but it can be done the other way. By the "rational root theorem", the only possible rational roots to this equation are \pm1, \pm 2, \pm 11, or \pm 22, the various factors of 22. By simply putting those numbers into f(x), it is easy to see that the only rational root is x= 2. That tells us that x-2 is a factor. Divide x^3+ 7x- 22 by x- 2 to find the other (quadratic) factor. You can solve that using the quadratic formula and use those roots to find the two other linear factors.
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