IST THE POSSIBLE RATIONAL ZEROS OF THE FUNCTION. 1. \( f(x)=6 x^{4}+4 x^{3}-10 x-27 \)

To find the possible rational zeros of the function \( f(x) = 6x^4 + 4x^3 - 10x - 27 \), we can use the Rational Root Theorem. According to the Rational Root Theorem, the possible rational zeros of a polynomial function are the factors of the constant term divided by the factors of the leading coefficient. Given function: \( f(x) = 6x^4 + 4x^3 - 10x - 27 \) The constant term is -27, and the leading coefficient is 6. Factors of the constant term (-27): ±1, ±3, ±9, ±27 Factors of the leading coefficient (6): ±1, ±2, ±3, ±6 Therefore, the possible rational zeros are the combinations of these factors. The possible rational zeros are: ±1, ±3, ±9, ±27, ±1/2, ±3/2, ±1/3, ±3/3, ±1/6, ±3/6 These are the possible rational zeros of the function \( f(x) = 6x^4 + 4x^3 - 10x - 27 \).