Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

Question

f(x) = -2x^4 + 4x^3 + 3x^2 + 18 Show work to receive credit. 

Answer 1

Given function is

The leading cofficient is 4 and constant term is 18

The factors of 18 is 1 , 2 , 3 , 6 , 9 , 18

The factors or 4 is 1 , 2 , 4

The list of possible rational zeros of the given function is

 

 

                                                    

Answer 2

Identify Rational Zeros :

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

Rational Root Theorem, if a rational number in simplest form p/q is a root of the polynomial equation a_nxⁿ + a_n – 1x^{n – 1} + ... + a₁x + a₀ = 0, then p is a factor of a₀ and q is a factor if a_n.

The function  f(x) = - 2x⁴ + 4x³ + 3x² + 18.

If p/q is a rational zero, then p is a factor of 18 and q is a factor of 2.

The possible values of p are   ± 1, ± 3, and ± 6.

The possible values for q are ± 1 and ± 2.

By the Rational Roots Theorem, the only possible rational roots are, p/q = ± 1/2, ± 1, ± 3/2, ± 3, and ± 6.