What is the quotient of d-2 / d4-6d3+d+17=   a. d3− 4d2 + 9d + 35 b. d3− 8d2 + 17d –17 c. d3− 8d2 + 16d − 31 r 79 d. d3– 4d2– 8d –15 r–13

Refer to the diagram below

We have (d⁴-6d³+d+17) ÷ (d-2)

Step 1:
Multiply d by a term that would give result of d⁴
The aim of this working out is to eliminate on one term at a time, starting from the highest polynomial

We have d⁴ ÷ d = d³ (Write this on the top)

Step 2:
Multiply back d³ by (d - 2) to get d⁴ - 2d³

Step 3:
Then subtract (d⁴ - 2d³) from (d⁴ - 6d³ + 0d² + d + 17) 
Notice that the term d⁴ is now eliminated
We have (-6d³ - -2d³) = (-4d³)
Then pull down the third term which is 0d²
We have the sum -4d³ + 0d²

Step 4:
Divide (-4d³) by (d) to get (-4d²)
Write (-4d²) next to (d³) on the top

Step 5:
Then multiply back (-4d²) by (d - 2) to get (-4d³+8d²)

Step 6:
Subtract (-4d³+8d²) from (-4d³ + 0d²) to get (-8d²) then pull down the next term (d) to make the sum (-8d² + d)
Notice that the term -4d³ is now eliminated

Step 7:
Divide -8d² by d to get -8d
Write -8d on the top, next to d³ - 4d²

Step 8:
Multiply back (-8d) by (d - 2) to get (-8d² + 16d)

Step 9:
The subtract  (-8d² + 16d) from (-8d + d) to get (-15d + 17)
Notice that the term (-8d²) has been eliminated
The last step is to divide -15d by d to get -15
Write -15 on the top next to the sum d³ - 4d² - 8d
Then multiply -15 by (d-2) to get -15d + 30
Subtract (-15d + 30) from (-15d + 17) to get a REMAINDER of 13

The answer is d³ - 4d² - 8d - 15 R 13
OPTION D