Verified answer

4y^4+2y^2-4y+12

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

y+2

step 1 divide 4y^4 by y

step 2 multiply 4y^3 by y+2. Multiply this result by -1

step 3 add to the original equation

.........4y^3

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

y+2 | 4y^4 + 2y^2 - 4y + 12

........-4y^4 - 8y^3

..................- 8y^3 + 2y^2 -4y +12

step 4 divide -8y^3 by y

step 5 multiply -8y^2 by y+2. Multiply this result by -1

step 6 add

.........4y^3 - 8y^2

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

y+2 | 4y^4 + 2y^2 - 4y + 12

........-4y^4 - 8y^3

..................- 8y^3 + 2y^2 -4y +12

..................+ 8y^3 + 16y^2

.................................18y^2 - 4y + 12

step 7 divide 18y^2 by y

step 8 multiply 18y by y+2. Multiply this result by -1

step 9 add

.........4y^3 - 8y^2 + 18y

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

y+2 | 4y^4 + 2y^2 - 4y + 12

........-4y^4 - 8y^3

..................- 8y^3 + 2y^2 -4y +12

..................+ 8y^3 + 16y^2

.................................18y^2 - 4y + 12

................................-18y^2 - 36y

...........................................- 40 y + 12

step 10 divide -40y by y

step 11 multiply -40 by y+2. Multiply this result by -1

step 12 add

.........4y^3 - 8y^2 + 18y - 40

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

y+2 | 4y^4 + 2y^2 - 4y + 12

........-4y^4 - 8y^3

..................- 8y^3 + 2y^2 -4y +12

..................+ 8y^3 + 16y^2

.................................18y^2 - 4y + 12

................................-18y^2 - 36y

...........................................- 40y + 12

...........................................+ 40y + 80

..............92

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....

(4y^4 + 0y^3 + 2y^2 - 4y + 12) / (y + 2)

4y^4 / y => 4y^3

4y^3 * (y + 2) = 4y^4 + 8y^3

4y^4 + 0y^3 - 4y^4 - 8y^3 = -8y^3

-8y^3 / y => -8y^2

-8y^2 * (y + 2) = -8y^3 - 16y^2

-8y^3 + 2y^2 + 8y^3 + 16y^2 = 18y^2

18y^2 / y => 18y

18y * (y + 2) = 18y^2 + 36y

18y^2 - 4y - 18y^2 - 36y => -40y

-40y / y = -40

-40 * (y + 2) = -40y - 80

-40y + 12 + 40y + 80 = 92

4y^3 - 8y^2 + 18y - 40/(y + 2)