List all the possible rational zeros of
f(x)=3x^3-x^2+2x=2.
Please help me. I don't understand how to do this. Can someone show me please.
To find the possible rational zeros of a polynomial function, you can use the Rational Root Theorem. The Rational Root Theorem states that if a rational number, p/q, is a zero of a polynomial function, then p must be a factor of the constant term (in this case, 2), and q must be a factor of the leading coefficient (in this case, 3).
For the given polynomial function: f(x) = 3x^3 - x^2 + 2x - 2
Step 1: Identify the factors of the constant term (2): ±1, ±2
Step 2: Identify the factors of the leading coefficient (3): ±1, ±3
The possible rational zeros of the given function are formed by taking the ratio of each factor of the constant term to each factor of the leading coefficient:
±1/1, ±1/3, ±2/1, ±2/3
In other words, the possible rational zeros are: ±1, ±1/3, ±2, ±2/3.
These are all the possible rational zeros of the given function. To determine which of these are actual zeros, you would need to use polynomial division or synthetic division to test the potential zeros and find the actual zeros of the function.