Can someone walk me through this question step by step. I have no idea how to solve it.
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.
possible rational zeros are combinations of
... all factors of the constant term ... 10 in this case
... divided by all factors of the highest order coefficient ... 2 in this case
don't forget negative factors
±10 , ±5 , ±2 , ±1 ... divided by ... ±2 , ±1
okay thank you!!
Certainly! I'll walk you through this question step by step.
Step 1: Understand the Rational Zero Theorem
The Rational Zero Theorem states that if a rational number (in the form p/q) is a zero of a polynomial function, then p must be a factor of the constant term and q must be a factor of the leading coefficient. In this case, the constant term is 10, and the leading coefficient is 2.
Step 2: Identify the possible factors of the constant term
To find the possible factors of the constant term (10), you need to consider all the positive and negative divisors of 10. These are 1, -1, 2, -2, 5, and -5.
Step 3: Identify the possible factors of the leading coefficient
Similarly, you need to find the factors of the leading coefficient (2). The factors of 2 are 1 and 2, as both are integers.
Step 4: Combine the factors to find the possible rational zeros
Now, you combine the factors obtained in steps 2 and 3 to determine all the possible rational zeros. The possible rational zeros are found by forming fractions of the form p/q using the factors obtained in the previous steps. For example, if the factors of the leading coefficient are 1 and 2, and the factors of the constant term are 1, -1, 2, -2, 5, and -5, then possible rational zeros could be 1/1, 1/-1, 1/2, 1/-2, 1/5, 1/-5, 2/1, 2/-1, 2/2, 2/-2, 2/5, and 2/-5.
Step 5: List all the possible rational zeros
In this step, you simply write down all the possible rational zeros that you found in the previous step. For the given polynomial, the possible rational zeros are 1, -1, 2, -2, 1/2, -1/2, 1/5, -1/5, 2/5, and -2/5.
And that's it! You have completed the steps to determine all the possible rational zeros of the given polynomial using the Rational Zero Theorem. Please note that this process only provides a list of possible rational zeros and does not guarantee that any of them are actual zeros of the polynomial.