SOLUTION: For the function below neatly solve for x. Show all work. 𝑓(𝑥) = 6𝑥^3 + 25𝑥^2 − 24𝑥 + 5 Once you have the function down to a factorable function, either factor

Algebra ->  Rational-functions -> SOLUTION: For the function below neatly solve for x. Show all work. 𝑓(𝑥) = 6𝑥^3 + 25𝑥^2 − 24𝑥 + 5 Once you have the function down to a factorable function, either factor       Log On


   

Question 1148163: For the function below neatly solve for x. Show all work.
𝑓(𝑥) = 6𝑥^3 + 25𝑥^2 − 24𝑥 + 5
Once you have the function down to a factorable function, either factor (if possible or use the quadratic formula to find the remainder of the zeros (real and/or imaginary).
Be sure that the number of solutions matches the degree. Put solutions in a
solution box (i.e. write all solutions together and circle/box them)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


By trial and error with from a list of the possible rational roots -- or, much better, by finding the roots with a graphing calculator -- determine that one root is -5. Then reduce the polynomial using synthetic division.

    -5  |  6  25  -24   5
        |    -30   25  -5
        +-----------------
           6  -5    1   0

So

6x%5E3%2B25x%5E2-24x%2B5+=+%28x%2B5%29%286x%5E2-5x%2B1%29

Then the quadratic factors nicely: 6x%5E3%2B25x%5E2-24x%2B5+=+%28x%2B5%29%283x-1%29%282x-1%29

And so the roots are -5, 1/3, and 1/2.