Answer:
12x^3 + 24x^2 + 48x + 104 + (5081/x-2)
Explanation:
12x^4 + 17* (17*17) + 8x -40/ x-2
1. remove the parenthesis
12x^4 + !7 * 17 * 17 + 8x -40 / x-2
2. multiply 17 by 17
12x^4 + 289 * 17 + 8x -= 40 /x-2
3. multiply 289 by 17
12x^ = 4913 + 8x - 40 / x-2
4. move 4913
12x^4 + 8x + 4913 - 40 / x-2
5. subtract 40 from 4913
12x^4 + 8x + 4873 / x-2
6. set up polynomials to be divided. if there is not a term for every exponent, insert one with a value of 0
x-2 into 12x^4 + 0x^3 + 0x^2 + 8x + 4873
7. divide the highest order term in the dividend 12x^4 by the highest order term in divisor x = 12x^3
8. multiply by new quotient term
12x^3 * x-2 = 12x^4 -24x^3
9. 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^3
10. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend
+24x^3
11. pull the next term from the original dividend down into the current dividend
+24x^3 + 0x^2
12. divide the highest order term in the dividend 24x^3 by the highest order term in divisor x = 24x^2
12x^3 + 24x^2
13. multiply new quotient by the divisor
24x^3 * x-2 = 24x^3 - 48x^2
14. the expression needs to be subtracted from the dividend, so change all the signs in 24x^3 - 48x^2
24x^3 + 0x^2 - 24x^3 + 48x^2
15. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend
+48x^2
16. pull the next terms from the original dividend down to the current dividend
+ 48x^2 + 8x
17. divide the highest order term in the dividend 48x^2 by the highest order term in the divisor = 48x
12x^3 + 24x^2 + 48x
18. multiply the new quotient term by the divisor
48x * x - 2 = 48x^2 - 96x
19. the expression needs to be subtracted from the dividend, so change all the signs in 48x^2 - 96x
-48x^2 + 96x
20. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend
48x^2 + 8x - 48x^2 + 96x
= 104x
21. pull the next terms from the original dividend down to the current dividend
+ 104x + 4873
22. divide the highest order term in the dividend 104x by the highest order term in the divisor x = 104
23. divide the new quotient by the divisor
104 * x -2 = 104x - 208
24. the expression needs to be subtracted from the dividend, so change all the signs in 104x - 208
104x + 4873 - 104x + 208 = 5081
25. the final answer is the quotient plus the remainder over the divisor
12x^3 + 24x^2 + 48x + 104 + (5081 / x - 2)