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14 November, 10:53

Divide 12x^4+17^3+8x-40 by x-2

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  1. 14 November, 12:38
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    12x^3 + 24x^2 + 48x + 104 + (5081/x-2)

    Step-by-step 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)
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