Question 1054916: find the linear factors of 27x^3-7x^2-x-30
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Use rational roots theorem to make a list of all possible roots to test, and then perform synthetic division, cutting down the factors to examine each time.
 , possible roots.
p the plusses and minuses of 1, 2, 3, 5, 6, 10, 15, 30
q the pluses and minuses of 1, 3, 9, 27
ONLY ONE real root near 1.143, so two of the roots will be complex.
You will probably find none of the rational possibilities will be near enough to 1.143, so the one real root is irrational. You will not find a linear factorization.
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