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
Accepted Solution
A:
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