Verified answer

(3x^3-x^2+x-2)/(x^2) = 3x^3/x^2 - x^2/x^2 + x/x^2 - 2/x^2 which is either

3x-1+ (1/x)-(2/x^2) or

3x-1 + x^-1 - 2x^-2 or

3x-1 + (x-2)/x^2

For -3x^4-2x-1 divided by x-1 you can use either

synthetic division or long division

Synthetic Division

1 | -3 0 0 -2 -1

-3 -3 -3 -5

------------------

-3 -3 -3 -5 -6

Long Division

-3x^3-3x^2-3x-5

--------------------------------

x-1 | -3x^4+0x^3+0x^2-2x-1

-3x^4+3x^3

----------------

-3x^3+0x^2

-3x^3+3x^2

-----------------

-3x^2-2x

-3x^2+3x

---------------

-5x-1

-5x+5

---------

-6

So your answer is -3x^3-3x^2-3x-5-(6/x-1)

If it was 3x^4-2x-1 then you wouldn't have had

a remainder and the answer would have been 3x^3+3x^2+3x+1

Note: The division ASCII is a little weird looking, but the math is there

Assumption: You need to use polynomial division instead of synthetic division.

..... 3x - 1

... ______________

x² ) 3x³ - x² + x - 2 <=== since 3x³ / x² = 3x, write 3x above 3x³

.... -3x³ <== subtract x² * 3x

.... -------------

........... -x² <== since -x² / x² = -1, write - 1 above -x²

........... +x² <== subtract x² * -1

........... ------

.................. x - 2 <== since you cannot go further, this is your remainder

ANSWER: (3x³ - x² + x - 2) / x² = 3x - 1 R x - 2

CHECK:

x²(3x - 1) + x - 2 =

x²(3x) + x²(-1) + x - 2 =

3x³ - x² + x - 2

true

~~~~~~~~~~~~~~~~~

Hint: Add the assumed 0 terms.

........ -3x³ - 3x² - 3x - 5

....... _______________________

x - 1 ) -3x^4 + 0x³ + 0x² - 2x - 1 <=== since -3x^4 / x = -3x³, write -3x³ above -3x^4

........ +3x^4 - 3x³ <== subtract -3x³ * (x - 1)

........ ------------------

................... -3x³ + 0x² <=== since -3x³ / x = -3x², write -3x² above 0x³

................... +3x³ - 3x² <== subtract -3x² * (x - 1)

................... ----------------

........................... -3x² - 2x <=== since -3x² / x = -3x, write -3x above 0x²

........................... +3x² - 3x <== subtract -3x * (x - 1)

........................... ---------------

..................................... -5x - 1 <== since -5x / x = -5, write - 5 above -2x

..................................... +5x - 5 <== subtract -5 * (x - 1)

..................................... -----------

.............................................. -6 <== since you cannot go further, this is your remainder

ANSWER: (-3x^4 - 2x - 1) / (x - 1) = -3x³ - 3x² - 3x - 5 R -6

CHECK:

(x - 1)(-3x³ - 3x² - 3x - 5) - 6 =

x(-3x³) + x(-3x²) + x(-3x) + x(-5) - 1(-3x³) - 1(-3x²) - 1(-3x) - 1(-5) - 6 =

-3x^4 - 3x³ - 3x² - 5x + 3x³ + 3x² + 3x + 5 - 6 =

-3x^4 + (-3x³ + 3x³) + (-3x² + 3x²) + (-5x + 3x) + (5 - 6) =

-3x^4 + 0 + 0 + (-2x) + (-1) =

-3x^4 - 2x - 1

true

(x+2)*(2r-9)= 2r^2-9r+4r-18 which simplifies to (2r^2-5r-18) then subtract z: (2r^2-5r-18) +(dispensed damaging into z) (-r^2 -17r -30) will become (r^2-22r-40 8) then divide x (classes are spacing to make it look like branch) ............_r_-_24__ ....(r+2)/ r^2-22r-40 8 ...........-(r^2+2r) ..................-24r-40 8 .................-(-24r-40 8) ...........................0 no the rest so which you will desire to get (r-24)