Determine the possible number of zeros, the number of \( x \)-intercepts, the number of turning points and the end behavior or the function. \( \begin{array}{ll}\text { 17) } 27 x^{9}+8 x^{6}-27 x^{3}-8=0 & \text { 18) } 3 x^{5}+9 x^{4}+34 x^{3}+102 x^{2}+63 x+189=0\end{array} \)

For the function \( f(x) = 27x^9 + 8x^6 - 27x^3 - 8 \), we can find that the maximum possible number of zeros is 9, based on the degree of the polynomial. The number of \( x \)-intercepts is equal to the number of real roots, which could be fewer than 9 depending on the actual solutions. As for turning points, the function can have up to 8 turning points, since a polynomial of degree \( n \) can have at most \( n-1 \) turning points. The end behavior shows that as \( x \) approaches positive or negative infinity, the function will go to positive infinity, since the leading term \( 27x^9 \) dominates and is positive. Now let's investigate the second function \( g(x) = 3x^5 + 9x^4 + 34x^3 + 102x^2 + 63x + 189 \). This polynomial has a degree of 5, indicating a maximum of 5 zeros. However, the actual number of \( x \)-intercepts will depend on the nature of the roots, which may be complex. Turning points can reach up to 4, and for the end behavior, as \( x \) approaches positive or negative infinity, this function will go to positive infinity as well, since the leading term \( 3x^5 \) is positive.