Question 1131131
Rational Roots Theorem indicates possible roots to check are -27, -9, -3, -1, 1, 3, 9, 27.


Try using synthetic division to check for any or all of them.  Remainder 0 means, the checked value is a root of the given polynomial.


x-3 factor is   the root or zero,  3.

<pre>
3   |   1   -4   -6   36   -27
    |       3    -3  -27    27
    |____________________________
        1   -1   -9   9      0

Test again using the resulting coefficients from that result.


3    |    1   -1   -9   9
     |   
     |         3    6  -9
     |____________________________
         1    2    -3   0

Resulting coefficients now mean  {{{x^2+2x-3}}}
which factorizes as  {{{(x+3)(x-1)}}}

</pre>
The full factorization of the given polynomial  is  {{{highlight((x-3)^2(x+3)(x-1))}}}.