# Use the rational zeros theorem

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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

• Use the rational zeros theorem -

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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