Use the Rational Zero Theorem to list all the possible rational zeros of
f(x) = 2x^4 + 3x^3 - 9x^2 + 3x + 10
DO NOT attempt to find the zeros.
If any rational roots of the form p/q exist, then
p is a factor of 10
q is a factor of 2
So, list all possible such fractions.
To use the Rational Zero Theorem to list all the possible rational zeros of a polynomial function, we need to consider the factors of the constant term and the leading coefficient.
In this case, the given polynomial function is f(x) = 2x^4 + 3x^3 - 9x^2 + 3x + 10. The constant term is 10, and the leading coefficient is 2.
The Rational Zero Theorem states that the possible rational zeros will be of the form p/q, where p represents a factor of the constant term (10 in this case), and q represents a factor of the leading coefficient (2 in this case).
To list all the possible rational zeros, we need to find all the factors of 10 and 2:
Factors of 10: ±1, ±2, ±5, ±10
Factors of 2: ±1, ±2
Combining the factors, we obtain the following possible rational zeros:
±1/1, ±2/1, ±5/1, ±10/1, ±1/2, ±2/2
Simplifying the fractions where possible, we have:
±1, ±2, ±5, ±10, ±1/2
So, the possible rational zeros of the given polynomial function are ±1, ±2, ±5, ±10, and ±1/2.