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Math Help - Long & synthetic division

  1. #1
    Newbie Jadekingy's Avatar
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    Long & synthetic division

    Hi Guys!

    I'm new - very glad I found this. I have a prescribed textbook for my math course - in the back they only give you answers to the problems but do not show how they got the answer - so its difficult to trace your steps and see where you went wrong. Which explains me being stuck with these 3 problems.

    I'll explain :

    Long or synthetic division can be used for this one:

    2x^4 - X^3 + 9x^2 divided by x^2 + 4

    When I do the above one, I get to a point where I have powers that arent the same so I can't minus - all the ways I try it I either get stuck where I can't divide more or I get a wrong answer than that in the book - I'd like to see what answer some of you get, maybe the book is wrong. Please type our your steps - Im desperate to see where I go wrong.

    Okay this one you have to use long division - again I get a horribly wrong answer if compared to the back of the book:

    6x^3 + 2x^2 + 22x divided by 2x^2 + 5


    The one below must be done using synthetic division - again my answer is wrong compared to the back of my textbook and I can't seem to understand why or how:

    x^3 + 2x^2 + 2x + 1 divided by x + 2


    I would appreciate your help a lot I'm either overlooking something or the book is wrong and Im very keen to find out which!

    Thanks!

    Janine
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  2. #2
    Super Member

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    Hello, Janine!

    You need to leave spaces for "missing terms" . . .


    (2x^4 - x^3 + 9x^2) \div (x^2 + 4)

    . . \begin{array}{ccccccc}<br />
& & & & 2x^2 & -x & +1 \\<br />
& & -- & -- & -- & -- & -- \\<br />
x^2+4 & ) & 2x^4 & -x^3 & +9x^2 \\<br />
& & 2x^4 & & + 8x^2 \\<br />
& & -- & -- & -- \\<br />
& & & -x^3 & +x^2 \\<br />
& & & -x^3 & & -4x \\<br />
& & & -- & -- & -- \\<br />
& & & & x^2 & + 4x \\<br />
& & & & x^2 & & +4 \\<br />
& & & & -- & -- & -- \end{array}
    . . . . . . . . . . . . . . . . . . . . 4x\quad-4


    Answer: . 2x^2 - x + 1 + \frac{4x-4}{x^2+4}




    (6x^3 + 2x^2 + 22x) \div (2x^2 + 5)

    . . \begin{array}{cccccc}<br />
& & & & 3x &+ 1 \\<br />
& & -- & -- & -- & -- \\<br />
2x^2+5 & ) & 6x^3 & +2x^2 &+ 22x \\<br />
& & 6x^3 & & +15x \\<br />
& & -- & -- & -- \\<br />
& & & 2x^2 & +7x \\<br />
& & & 2x^2 & & +5 \\<br />
& & & -- & -- & -- \\<br />
& & & & 7x & -5 \end{array}


    Answer: . 3x + 1 + \frac{7x-5}{2x^2 + 5}




    (x^3 + 2x^2 + 2x + 1) \div (x + 2)


    . . \begin{array}{cccccc}<br />
-2 & | & 1 & 2 & 2 & 1 \\<br />
& | & & \text{-}2 & 0 & \text{-}4 \\<br />
& & --&--&--&-- \\<br />
& & 1 & 0 & 2 & \text{-}3 \end{array}


    Answer: . x^2 + 2 - \frac{3}{x+2}

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