MATH SOLVE

2 months ago

Q:
# 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

The answer is d³ - 4d² - 8d - 15 R 13

OPTION D

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