SOLUTION: Find all of the rational zeros of each function 26. p(x)= x^3+3x^2-25x+21 p= (+or-)1, (+or-)3, (+or-)7, (+or-)21 q= (+or-)1 1/1 1/3, 1/7, 1/21

Algebra ->  Rational-functions -> SOLUTION: Find all of the rational zeros of each function 26. p(x)= x^3+3x^2-25x+21 p= (+or-)1, (+or-)3, (+or-)7, (+or-)21 q= (+or-)1 1/1 1/3, 1/7, 1/21      Log On


   

Question 187079This question is from textbook algebra2
: Find all of the rational zeros of each function
26. p(x)= x^3+3x^2-25x+21
p= (+or-)1, (+or-)3, (+or-)7, (+or-)21
q= (+or-)1
1/1 1/3, 1/7, 1/21 This question is from textbook algebra2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Any rational zero can be found through this equation

where p and q are the factors of the last and first coefficients


So let's list the factors of 21 (the last coefficient):



Now let's list the factors of 1 (the first coefficient):



Now let's divide each factor of the last coefficient by each factor of the first coefficient









Now simplify

These are all the distinct rational zeros of the function that could occur




Note: these are all of the possible roots. To find the actual rational roots (if there are any), you need to plug each possible root into the given polynomial. If you get a result of 0, then the corresponding input is a zero.