I have been told that to find factors of a polynomial (nth degree) we have to find the factors of constant term and that of coefficient of leading term of the polynomial in concern.
The possible integral zeros of the polynomial will be from the factor set of the constant term while rational zeros would be from set of each factor of constant / each factor of coefficient of the leading term.
Now I have to replace one by one value of $X$ for each integral and rational factors founded above and check if the polynomial results to $0$ (zero). The issue is that I go into deep / lengthy calculation if suppose constant term is $140$ and coefficient of leading term is $6$ per say.
Factors of $140 = -1,+1,-2,+2,-4,+4,-5,+5,-7,+7,.....$
Factors of $6 = -1,+1,-2,+2,-3,+3,-6,+6 $
Integral roots of the polynomial (set range) = $-1,+1,-2,+2,-4,+4,-5,+5,-7,+7,.....$
Rational roots of the polynomial (set range) = $(-1,+1,-2,+2,-4,+4,-5,+5,-7,+7,.....)/ (-1,+1,-2,+2,-3,+3,-6,+6 )$
Taking one by one value and testing for zero is a very lengthy time consuming method - is there a quick easy way to find zeros of the pronominal?