\( \begin{array}{lll}\text { The expression } 9 x^{3}-12 x^{2}-11 x-19 \text { divided by } \\ 3 x-5 \text { equals } a x^{2}+b x+c+\frac{R}{3 x-5}, & \text { where } \\ a= & b= & c= \\ 3 & \\ & \end{array} \)

When you divide \( 9x^3 - 12x^2 - 11x - 19 \) by \( 3x - 5 \), you can start by using polynomial long division. By dividing the leading term of the dividend by the leading term of the divisor, you'll get the first term of the quotient. Continue this process until you reach the remainder. You will find that \( a = 3 \), \( b = -1 \), and \( c = -4 \). For verification, you can substitute your values of \( a \), \( b \), and \( c \) back into the expression and reconstruct the original polynomial to ensure that everything checks out correctly—this is a handy way to avoid mistakes in your calculations and confirm your results!