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How do I find the zeros after the synthetic division?

How do I find the zeros after the synthetic division?-example-1
User Esynce
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Given the function:


f(x)=x^3+5x^2+2x-8

We know that x = 1 is a zero of the polynomial, so taking the division:

Then, we can rewrite the polynomial as:


f(x)=(x-1)(x^2+6x+8)

Now, for the quadratic term:


x^2+6x+8=(x+2)(x+4)

Then:


f(x)=(x-1)(x+2)(x+4)

Finally, the other zeros of the function are:


\begin{gathered} x+2=0\Rightarrow x=-2 \\ x+4=0\Rightarrow x=-4 \end{gathered}

How do I find the zeros after the synthetic division?-example-1
User Metaphore
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