calculus

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Find the complex zeros of the polynomial function. Write f in factored form.

f(x)=3x^4-10x^3-12x^2+122x-39

Please show wrok, I do not understand how to do this.

  • calculus -

    The 39 and 3 tempt me to try roots like 1,3,1/3. Go for the low-hanging fruit first

    use synthetic division to find that

    f(-3)=0, so
    f(x) = (x+3)(3x^3-19x^2+45x-13)
    f(1/3) = 0, so
    f(x) = (x+3)(3x-1)(x^2-6x+13)
    there are no more real roots

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