How do you find rational zeros
Use the Rational Roots Theorem.
The Rational Zeros Theorem states:
If P(x) is a polynomial with integer coefficients and if is a zero of P(x) ( P() = 0 ), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x) .
In other words, fllow these steps:
1) Arrange the polynomial in descending order
2) Write down all the factors of the constant term. These are all the possible values of p .
3) Write down all the factors of the leading coefficient. These are all the possible values of q .
4) Write down all the possible values of p/q . Remember that since factors can be negative, + and - must both be included. Simplify each value and cross out any duplicates.
5) Use synthetic division to determine the values of for which P(x) = 0 . These are all the rational roots of P(x) .