Use the Rational Zeros Theorem to find all the rational zeros of a polynomial. Follow these steps:
1) Arrange the polynomial in descending order: f(x) = x⁴ + 2x³ – 3x²
– 4x + 20
2) Identify all the factors of the constant term. These are all the possible values of p .
1 x 20 ; 2 x 10 ; 4 x 5
possible values of p: 1, 2, 4, 5, 10, 20
3) Identify all the factors of the leading coefficient. These are all the possible values of q.
leading coefficient = 1. value of q = 1
4) Identify all the possible values of p/q . Factors can be positive and negative, so, p/q and -p/q must both be included. Simplify each value and cross out any duplicates.
p/q = 1/1 ; 2/1 ; 4/1 ; 5/1 ; 10/1 ; 20/1
-p/q = -1/1 ; -2/1 ; -4/1 ; -5/1 ; -10/1 ; -20/1
Possible rational zeros of f(x) = x⁴ + 2x³ – 3x² – 4x + 20 are:
± 1, ± 2, ± 4, ± 5, ± 10, ± 20