Algebra

Divide using long division: 6x3 + 19x2 + x – 10 divided by 2x -1

Divide using synthetic division: 2x3 + 2x2 + 10 divided by x + 3

PLEASE HELP!

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  1. ans.__________________
    2x-1| 6x^3 +19 x^2 +x -10

    ans. 3 x^2
    ________________________
    2x-1| 6x^3 +19 x^2 +x -10
    ______6x^3 ______________


    ans. 3 x^2
    ________________________
    2x-1| 6x^3 +19 x^2 +x -10
    ______6x^3 - 3 x^2 ______________
    _______0 +22 x^2 +x -10

    ans. 3 x^2 +11 x
    ________________________
    2x-1| 6x^3 +19 x^2 +x -10
    ______6x^3 - 3 x^2 ______________
    _______ 0 +22 x^2 + x -10
    ___________+22 x^2 -11x____
    ___________________12x -10

    ans. 3 x^2 +11 x +6
    ________________________
    2x-1| 6x^3 +19 x^2 +x -10
    ______6x^3 - 3 x^2 ______________
    _______ 0 +22 x^2 + x -10
    ___________+22 x^2 -11x____
    ___________________12x -10
    ___________________12 x-6
    R = -4
    =============================
    _______2 2 0 10

    -3_________________________
    _______2

    _______2 2 0 10
    ________-6
    -3_________________________
    _______2

    _______2 2 0 10
    ________-6
    -3_________________________
    _______2 -4

    _______2 2 0 10
    ________-6 12
    -3_________________________
    _______2 -4

    _______2 2 0 10
    ________-6 12
    -3_________________________
    _______2 -4 12

    _______2 2 0 10
    ________-6 12 -36
    -3_________________________
    _______2 -4 12

    _______2 2 0 10
    ________-6 12 -36
    -3_________________________
    _______2 -4 12 -26
    so
    2x^2 -4x +12 remainder -26

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  2. I'm a little confused by this. What is the answer to #1 or is 2x^2-4x+12 remainder -26 the answer? If so then how do I solve for #2? I'm sorry just some things come out funny when typed.

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  3. The answer to #1 is 3x^2+11x+6 remainder -4
    Here is the last line of #1
    ans. 3 x^2 +11 x +6
    ________________________
    2x-1| 6x^3 +19 x^2 +x -10
    ______6x^3 - 3 x^2 ______________
    _______ 0 +22 x^2 + x -10
    ___________+22 x^2 -11x____
    ___________________12x -10
    ___________________12 x-6
    R = -4
    then I put a line like this
    ==================================
    and went on with the synthetic division.
    In both cases I tried to only put one thing at a time, so copied over and over getting a little further into the problem each time
    The answer to the synthetic division one is
    2 x^2 - 4x + 12 reminder is -26

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  4. Here is the final version of the synthetic division one:
    _______2 2 0 10
    ________-6 12 -36
    -3_________________________
    _______2 -4 12 -26
    so
    2x^2 -4x +12 remainder -26

    like bring the 2 down
    -3*that 2 = -6
    2-6 goes below as -4
    -3*-4 = +12 - that goes below the 0
    0+12 = 12, bring it down
    -3*12 = -36
    add that to 10 to get remainder of -26

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  5. 2x3 + 2x2 + 10
    By the way, important to write that as
    2x^3 +2x^2 + 0x + 10
    If you leave the zero coefficient terms of the polynomial out, you get messed up worse with columns and such. That is exactly why they had no coefficient of x, to make you figure that out.

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