Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. -2x^4+4x^3+3x^2+18
let f(x) = 2x^4 + 4x^3 + 3x^2 + 18
f(1) = 2+4+3+18 ≠ 0
f(-1) = 2 - 4 + 3 + 18≠0
f(2) ≠0
f(-2) ≠0
...
f(±9) ≠ 0
tried ±1, ±2, ±3, ±6, ±9, ±1/2, ± 3/2, ±9/2
none worked
could not find any rational factors
here is a nice youtube showing how it works
http://www.youtube.com/watch?v=hJCHhWlyIws
To find the possible rational zeros using the Rational Zeros Theorem, we need to consider the factors of the constant term (18) and the factors of the leading coefficient (-2).
The factors of 18 are ±1, ±2, ±3, ±6, ±9, and ±18.
The factors of -2 are ±1 and ±2.
Therefore, the possible rational zeros are as follows:
±1/1, ±2/1, ±3/1, ±6/1, ±9/1, ±18/1, ±1/2, ±2/2, ±3/2, ±6/2, ±9/2, and ±18/2.
Simplifying the expressions, we get:
±1, ±2, ±3, ±6, ±9, ±18, ±0.5, ±1, ±1.5, ±3, ±4.5,and ±9.
These are all the possible rational zeros of the function.
To find the possible rational zeros of the function -2x^4 + 4x^3 + 3x^2 + 18, we can use the Rational Zeros Theorem. This theorem states that if a polynomial has a rational zero, it must be of the form p/q, where p is a factor of the constant term (here, 18) and q is a factor of the leading coefficient (here, -2).
Step 1: Identify the factors of the constant term (18).
The factors of 18 are: ±1, ±2, ±3, ±6, ±9, and ±18.
Step 2: Identify the factors of the leading coefficient (-2).
The factors of -2 are: ±1 and ±2.
Step 3: Form all possible fractions using the factors obtained in steps 1 and 2.
The possible rational zeros are: ±1/1, ±1/2, ±2/1, ±2/2, ±3/1, ±3/2, ±6/1, ±6/2, ±9/1, ±9/2, ±18/1, ±18/2.
Simplifying these fractions, the possible rational zeros are: ±1, ±1/2, ±2, ±3, ±3/2, ±6, ±9, ±18.