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(6x^3+26x^2+16x−24)÷(x+3)

Guest Feb 24, 2017
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Simplify the following:
(6 x^3 + 26 x^2 + 16 x - 24)/(x + 3)

Factor 2 out of 6 x^3 + 26 x^2 + 16 x - 24:
2 (3 x^3 + 13 x^2 + 8 x - 12)/(x + 3)

The possible rational roots of 3 x^3 + 13 x^2 + 8 x - 12 are x = ± 1/3, x = ± 2/3, x = ± 4/3, x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = 2/3, x = -2 and x = -3 are roots. This gives 3 x - 2, x + 2 and x + 3 as all factors:
(2 (3 x - 2) (x + 2) (x + 3))/(x + 3)

(2 (3 x - 2) (x + 2) (x + 3))/(x + 3) = (x + 3)/(x + 3)×2 (3 x - 2) (x + 2) = 2 (3 x - 2) (x + 2):
Answer: |2(3x - 2) (x + 2)

Guest Feb 24, 2017

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