Answer:12x^3 + 24x^2 + 48x + 104 + (5081/x-2)Step-by-step explanation:12x^4 + 17* (17*17) + 8x -40/ x-21. remove the parenthesis12x^4 + !7 * 17 * 17 + 8x -40 / x-22. multiply 17 by 1712x^4 + 289 * 17 + 8x -= 40 /x-23. multiply 289 by 1712x^ = 4913 + 8x - 40 / x-24. move 491312x^4 + 8x + 4913 - 40 / x-25. subtract 40 from 491312x^4 + 8x + 4873 / x-26. set up polynomials to be divided. if there is not a term for every exponent, insert one with a value of 0x-2 into 12x^4 + 0x^3 + 0x^2 + 8x + 48737. divide the highest order term in the dividend 12x^4 by the highest order term in divisor x = 12x^38. multiply by new quotient term12x^3 * x-2 = 12x^4 -24x^39. the expression needs to be subtracted from the dividend, so change all the signs in 12x^4 - 24x^3 12x^4 + 0x^3 - 12x^4 + 24x^310. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend+24x^311. pull the next term from the original dividend down into the current dividend+24x^3 + 0x^212. divide the highest order term in the dividend 24x^3 by the highest order term in divisor x = 24x^212x^3 + 24x^213. multiply new quotient by the divisor24x^3 * x-2 = 24x^3 - 48x^214. the expression needs to be subtracted from the dividend, so change all the signs in 24x^3 - 48x^224x^3 + 0x^2 - 24x^3 + 48x^215. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend+48x^216. pull the next terms from the original dividend down to the current dividend+ 48x^2 + 8x17. divide the highest order term in the dividend 48x^2 by the highest order term in the divisor = 48x 12x^3 + 24x^2 + 48x18. multiply the new quotient term by the divisor48x * x - 2 = 48x^2 - 96x19. the expression needs to be subtracted from the dividend, so change all the signs in 48x^2 - 96x -48x^2 + 96x20. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend48x^2 + 8x - 48x^2 + 96x= 104x21. pull the next terms from the original dividend down to the current dividend+ 104x + 487322. divide the highest order term in the dividend 104x by the highest order term in the divisor x = 10423. divide the new quotient by the divisor104 * x -2 = 104x - 20824. the expression needs to be subtracted from the dividend, so change all the signs in 104x - 208104x + 4873 - 104x + 208 = 508125. the final answer is the quotient plus the remainder over the divisor12x^3 + 24x^2 + 48x + 104 + (5081 / x - 2)