Use the rational zeros theorem
posted by Alley .
Use the rational zeros theorem to list the potential reational zeros of the polynomial function. Do not attempt to find the zeros.
f(x)=6x^4+9x^3+30x^2+63x+28

Arrange the polynomial in descending order
Write down all the factors of the constant term. These are all the possible values of p .
Write down all the factors of the leading coefficient. These are all the possible values of q .
Write down all the possible values of . Remember that since factors can be negative, and  must both be included. Simplify each value and cross out any duplicates.
Use synthetic division to determine the values of for which P() = 0 . These are all the rational roots of P(x) .
factors of 28: 28,1; 14,7;and the negatives of those
facors of 6: 6,1;3,2 and the negatives of those.
now list all the p/q values, eliminating the duplicates.
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