Question 1049043
{{{4(2x^5+4x^4-5x^3+3)}}}


Review Rational Roots Theorem.  The possible roots to check, helpful for factoring, are the plusses and minuses of 1, 3, 1/2, 3/2; and you might expect as many as up to five complex roots.


Setup your first-root synthetic divisions this way:

<pre>
ROOT   |      2    4     -5     0     0     3
       |
       |
       |_____________________________________________


</pre>
Because you must account for all lower degree of the variable.


You will find that NONE of the possible rational roots checked will work; meaning remainder in the synthetic divisions will be NONZERO.  The factor {{{2x^5+4x^4-5x^3+3}}}  is the PRIME factor.



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I did not actually perform the divisions.  I used the graphing feature of Google Chrome browser.