Question

How do I find the zeros after the synthetic division?

Answer 1

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:

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