Question 339234: factor the following polymonial completely:
2x^3 + x^2 - 6x - 3
Answer by alanc(27)   (Show Source):
You can put this solution on YOUR website! 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
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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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