SOLUTION: 3x^4-4x^3+x^2+6x-2 a. State the degree of the polynomial. b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to list all of the p

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 3x^4-4x^3+x^2+6x-2 a. State the degree of the polynomial. b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to list all of the p      Log On


   

Question 1197410: 3x^4-4x^3+x^2+6x-2
a. State the degree of the polynomial.
b. State the number of zeros the polynomial function will have.
c. Use the Rational Zero Theorem to list all of the possible rational zeros
d. Use your calculator to determine which numbers in the list of rational zeros are probable rational
zeros.
e. Use synthetic division to verify one rational zero.
f. Use synthetic division or other algebraic methods to find all remaining zeros. List all of the zeros
of the polynomial function.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
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3x^4-4x^3+x^2+6x-2
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Degree obviously 4. In plain sight.
That means could be four zeros for the polynomial.

Possible Zeros? Just review and use the theorem and list the zeros yourself.

If you check with a graphing tool, you'll find zeros at -1, and something near to 0.33. This one could mean, 1%2F3 may be a zero.

You can use synthetic division yourself to check with the zero (root) of -1.

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3x^4-4x^3+x^2+6x-2
Check on poss. root -1. 
-1  |  3   -4   1   6   -2
   |
    |     -3    7  -8    2
    --------------------------------

       3   -7    8  -2   0

Meaning polynom,
%28x%2B1%29%283x%5E3-7x%5E2%2B8x-2%29

Check on poss. root +1/3. 
1/3   |    3    -7    8    -2
      |
      |          1   -2    2
      |___________________________
           3    -6    6    0

Meaning, polynom. is %28x%2B1%29%28x-1%2F3%29%283x%5E2-6x%2B6%29
Which can still be given further work,...