Divide.Use long dl vision. 7) (7r^3+41r^2+2r-17)div (7r+6) r^2+5r-7+(12)/(7r+6) B) y^2 C) r^2+5r-4+(7)/(7r+6)

To divide $(7r^{3}+41r^{2}+2r-17)$ by $(7r+6)$ using long division, we can follow these steps:<br /><br />1. Divide the first term of the dividend $(7r^{3})$ by the first term of the divisor $(7r)$ to get the first term of the quotient $(r^{2})$.<br /><br />2. Multiply the divisor $(7r+6)$ by the first term of the quotient $(r^{2})$ to get $7r^{3}+6r^{2}$.<br /><br />3. Subtract the result from the dividend to get a new dividend of $35r^{2}+2r-17$.<br /><br />4. Repeat the process by dividing the first term of the new dividend $(35r^{2})$ by the first term of the divisor $(7r)$ to get the next term of the quotient $(5r)$.<br /><br />5. Multiply the divisor $(7r+6)$ by the new term of the quotient $(5r)$ to get $35r^{2}+30r$.<br /><br />6. Subtract the result from the new dividend to get a new dividend of $-28r-17$.<br /><br />7. Repeat the process by dividing the first term of the new dividend $(-28r)$ by the first term of the divisor $(7r)$ to get the next term of the quotient $(-4)$.<br /><br />8. Multiply the divisor $(7r+6)$ by the new term of the quotient $(-4)$ to get $-28r-24$.<br /><br />9. Subtract the result from the new dividend to get a new dividend of $7$.<br /><br />10. Since the degree of the new dividend $(7)$ is less than the degree of the divisor $(7r+6)$, we stop here.<br /><br />The final quotient is $r^{2}+5r-4$ and the remainder is $\frac{7}{7r+6}$.<br /><br />Therefore, the correct answer is C) $r^{2}+5r-4+\frac{7}{7r+6}$.