The equation is $\"\"$ .

Rational Root Theorem, if a rational number in simplest form $\"\"$ is a root of the polynomial equation $\"\"$ , then $\"\"$ is a factor of $\"image\"$ and $\"\"$ is a factor if $\"image\"$ _.

Rational zeros method:

If $\"\"$ is a rational zero, then $\"\"$ is a factor of 8 and $\"\"$ is a factor of 1.

The possible values of $\"\"$ are $\"\"$ .

The possible values for q are $\"\"$ .

So, $\"\"$ .

Make a table for the synthetic division and test possible zeros.

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	1	-1	-2	-4	-8
1	1	0	2	-2	-10
2	1	1	4	4	0

Observe the table, $\"\"$ , solution of equation is 2.

The remaining equation is $\"\"$ .

$\"\"$

If $\"\"$ is a rational zero, then $\"\"$ is a factor of 4 and $\"\"$ is a factor of 1.

The possible values of $\"\"$ are $\"\"$ .

so, $\"\"$ .

Make a table for the synthetic division and test possible zeros.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	1	1	4	4
1	1	2	6	10
-1	1	0	4	0

Observe the table, $\"\"$ , solution of equation is 2.

The remaining equation is $\"\"$ .

If remaining equation is solved the solutions are in complex numbers.

Therefore , the solutions in real number system are $\"\"$ .

$\"\"$

The solutions of equation in real number system are $\"\"$ .