Posted by Math Loser :( on Monday, November 22, 2010 at 6:18am.
Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2.
(a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial.
(b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.

algebra  Reiny, Monday, November 22, 2010 at 7:51am
I should try x = ±1, ±2, ±2/3, and ±1/3
f(1) = 3272 ≠ 0
f(1) = 32+72 = 0 , so x+1 is a factor
f(2) = 24 8 + 14  2 ≠0
f(2) = 24  8  14  2 = 0 , so x2 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)(x2)(x+1)
x = 1, 1/3, and 2
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