Question

100 POINTS
Divide.
(4x^4-4x^2-x-3)/(2x^2-3)

Answer 1

We can use polynomial long division to divide (4x^4 - 4x^2 - x - 3) by (2x^2 - 3):

2x^2 + 0x - 1

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

2x^2 - 3 | 4x^4 + 0x^3 - 4x^2 - x - 3

4x^4 - 6x^2

-----------

2x^2 - x

2x^2 - 3

-------

x - 3

Therefore,

(4x^4 - 4x^2 - x - 3)/(2x^2 - 3) = 2x^2 + 0x - 1 with a remainder of (x - 3)/(2x^2 - 3).

So the final answer is

2x^2 - 1 + (x - 3)/(2x^2 - 3)

Answer 2

The result of the polynomial division is (4x⁴ - 4x² - x - 3) ÷ (2x² - 3) = (2x² + 5) - (x + 12)/(2x² - 3)

How to divide the polynomial

From the question, we have the following parameters that can be used in our computation:

(4x⁴ - 4x² - x - 3) ÷ (2x² - 3)

Using the long division method of quotient, we have

2x² - 3 | 4x⁴ - 4x² - x - 3

The division steps are as follows

2x² + 5

2x² - 3 | 4x⁴ - 4x² - x - 3

4x⁴ - 6x²

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

10x² - x - 3

10x² - 15

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

-x - 12

This means that

(4x⁴ - 4x² - x - 3) ÷ (2x² - 3) = (2x² + 5) - (x + 12)/(2x² - 3)