Posted by Math Loser :( on Monday, November 22, 2010 at 6:18am.
I should try x = ±1, ±2, ±2/3, and ±1/3
f(1) = 3-2-7-2 ≠ 0
f(-1) = -3-2+7-2 = 0 , so x+1 is a factor
f(-2) = -24 -8 + 14 - 2 ≠0
f(2) = 24 - 8 - 14 - 2 = 0 , so x-2 is a factor
f(2/3) = 8/9 - 8/9 - 14/3 - 2 ≠ 0
f(-2/3) = -8/9 - 8/9 + 14/3 - 2 ≠0
f(1/3) = 1/9 - 2/9 - 7/9 - 2 ≠ 0
f(-1/3) = -1/9 - 2/9 + 7/3 - 2 = 0 , so (3x+1) is a factor
3x^3 – 2x^2 – 7x – 2 = (3x+1)(x-2)(x+1)
x = -1, -1/3, and 2
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