Question

Fill in the missing values below one at a time to find the quotient when x, cubed, minus, 6, x, plus, 4x 3 −6x 4 is divided by x, minus, 2x−2.

Answer 1

The completed missing values are

4x² [ 0] - 1

x 4x³ - 8x² -x

-2 4x³ - 8x² -x

And the quotient is 4x² - 1

The functions are given as

4x³ - 8x² - x + 2

x - 2

These functions imply that:

Dividend = 4x³ - 8x² - x + 2

Divisor = x - 2

So, the quotient can be represented as

Quotient = Dividend/Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = (4x³ - 8x² - x + 2)/(x - 2)

For the missing values, we have

x 4x³

-2

Divide 4x³ by x

So, we have (complete the dividend)

4x²

x 4x³ -8x² -x + 2

-2

Solving further, we have

4x² -8x

x 4x³ -8x² -x + 2

-2 4x³ -8x²

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

-x + 2

Divide -x by x

So, we have

4x² - 1

x 4x³ -8x² -x + 2

-2 4x³ -8x²

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

-x + 2

-x + 2

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

0

This means that

Dividend = 4x³ - 8x² - x + 2

Divisor = x - 2

Quotient = 4x² -1

So, the completed boxes are

4x² [ 0] - 1

x 4x³ - 8x² -x

-2 4x³ - 8x² -x