<PRE><B>Question 339234</B>
If you notice,  x = -0.5  is a zero for this polynomial.  I am using a rule called the rational zeros theorem.  that the possible factors for this polynomial are the ratios of the factors of the last and first coefficients of the polynomial,  -3 and 2.   so -1/2 was one of the possibilities.

Since it is, factor it out, using synthetic division.

-1/2 |   2  1  -6  -3
         0  -1  0   3
_______________________
         2   0   -6  0

the quotient is (2x^2 -6)
It can be factored as  2*(x - sqrt(3))(x + sqrt(3))



2x^3 + x^2 - 6x - 3 = (x + 0.5)*2*(x - sqrt(3))(x + sqrt(3))

factors  : 2, (x + 0.5), (x - sqrt(3)), and (x + sqrt(3))



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