Step 1:

The equation is $\"\"$ .

Identify Rational Zeros

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

The equation is $\"\"$

If $\"\"$ is a rational zero, then $\"\"$ is a factor of 8 and $\"\"$ is a factor of 4.

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, $\"\"$ ,the remaining equation is $\"\"$ .

Step 2:

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

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

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, $\"\"$ , the remaining equation is $\"\"$ .

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

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

Solution:

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