SOLUTION: a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining

Question 1204769: a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x) = 2x^3 - 3x^2 - 11x + 6
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(a) constant term 6; leading coefficient 2. The possible rational zeros are

ANSWER: (plus or minus) 1, 2, 3, 6; 1/2, 3/2

(b) evaluating the polynomial at the possible roots is faster than testing each root using synthetic division. f(3) = 2(27)-3(9)-11(3)+6 = 0, so 3 is a root. Use synthetic division to find the polynomial that remains after the root x=3 is removed.


    +----------------
  3 | 2  -3  -11  6
    |     6    9 -6
    +----------------
      2   3   -2  0

ANSWER: 3 is a root

(c) The remaining polynomial is

ANSWER: The two other zeros are 1/2 and -2

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