Answer
Fill the blanks with
$-6$
and
$(x+6)(2x^{2}-x-1)=0$
Work Step by Step
When dividing a polynomial with (x-c) using synthetic division,
the last value of the last row is $f(c)$.
We have a polynomial equation $f(x)=0$.
from the synthetic division we see that $f(-6)=0$.
So, $-6$ is a zero of f, which means
it is a root of the equation.
Since $-6$ is a zero of f, $(x-(-6))=(x+6)$ is a factor of $f(x)$
The first three values of the last row
give coefficients of the quotient $f(x)\div(x+6)$
So we can write
$f(x)=(x+6)(2x^{2}-x-1)$, and the equation as
$(x+6)(2x^{2}-x-1)=0$
