How do you find the zeros of $x^3-x^2-10x-8$ ?

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Answer 1 · 2016-05-25T02:07:58

$x=$ Either -1 or -2 or +4

$f(x) = x^3-x^2-10x-8$

To find the zeros of this polynomial function we must find all values of x such that $f(x) = 0$

Notice that $f(x)$ factorises to $(x+1)(x^2-2x-8)$
Which further factorises to $(x+1)(x+2)(x-4)$

Hence the zeors of $f(x)$ occur when $(x+1)(x+2)(x-4) =0$

This occurs when either $(x+1)=0$ or $(x+2)=0$ or $(x-4)=0$

Therefore the zeros of $f(x)$ are either -1 or -2 or +4

How do you find the zeros of x^3-x^2-10x-8x^3-x^2-10x-8?