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

Algebra ->  Polynomials-and-rational-expressions -> 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       Log On


   

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
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(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 2x%5E2%2B3x-2

2x%5E2%2B3x-2=%282x-1%29%28x%2B2%29

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