SOLUTION: Use the Rational Zero Theorem to list the possible rational zeros of P(x)=3x^3 -4x^2 +7x -10. If you can show your work on how this problem was solved it will really help me t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Rational Zero Theorem to list the possible rational zeros of P(x)=3x^3 -4x^2 +7x -10. If you can show your work on how this problem was solved it will really help me t      Log On


   

Question 886915: Use the Rational Zero Theorem to list the possible rational zeros of
P(x)=3x^3 -4x^2 +7x -10.
If you can show your work on how this problem was solved it will really help me to learn. Thanks
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%22P%28x%29%22%22%22=%22%223x%5E3+-4x%5E2+%2B7x+-10.

The factors of the absolute value of the constant term,
-10, (which is |-10| or 10):

matrix%281%2C8%2C1%2C%22%2C%22%2C+2%2C%22%2C%22%2C+5%2C%22%2C%22%2C+and%2C+10%29

The factors of the absolute value of the coefficient of the 
leading term, 3, the term with the largest exponent,
which is |3| or 3: 

matrix%281%2C4%2C1%2C%22%2C%22%2C+and%2C+3%29
 
Now we make all the fractions possible using one of these 
1, 2, 5, and 10 as the numerator and one of these 1 and 3
as the denominator:



Reduce any of them if possible:



Put ± in front of each:



That's the list of all candidates for rational solutions.

Edwin