Question 1013109

Someone help please, it says. 

Use synthetic division to solve : x^5-4x^4-2x^3+4x^2+x=0 

Show work please. Thanks
<pre>{{{x^5 - 4x^4 - 2x^3 + 4x^2 + x = 0}}}
{{{x(x^4 - 4x^3 - 2x^2 + 4x + 1) = x(0)}}} --- Factoring out GCF, x
{{{x^4 - 4x^3 - 2x^2 + 4x + 1 = 0}}} -------- Factoring out GCF, x
Using the RATIONAL ROOT THEOREM we find that 2 roots are: {{{" "+- 1}}}

Use synthetic division with a divisor/root of 1
  1 |  1  - 4  - 2  +  4  +  1
    |     + 1  - 3  -  5  -  1 
    --------------------------
       1  - 3  - 5  -  1     0</pre>

Now we have: {{{x^3 - 3x^2 - 5x - 1 = 0}}}

<pre>
Use synthetic division with a divisor/root of - 1
- 1 |  1  - 3  - 5  -  1
    |     - 1  + 4  +  1 
  ----------------------
       1  - 4  - 1     0</pre>

Now we have: {{{x^2 - 4x - 1 = 0}}}

<pre>{{{x^2 - 4x - 1}}} does not have any INTEGER roots, so you can use the following to get the final 2 roots:
1) the quadratic equation
2) completing the square
3) graphing</pre>