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September 17, 2014

September 17, 2014

Posted by **Math Loser :(** on Monday, November 22, 2010 at 6:18am.

(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 7:51amI 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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