Question

Divide. (4x4 - 4x2 – x-3) = (2x2 – 3)

Answer 1

Given:

Division problem:

$(4x^4-4x^2-x-3)\div (2x^2-3)$

To find:

The solution for the given division problem.

Solution:

We have,

$(4x^4-4x^2-x-3)\div (2x^2-3)$

Here, 4x^4-4x^2-x-3 is the dividend and (2x^2-3) is divisor.

Using the long division method we get

$\underline{2x^2-3}|\overline{4x^4-4x^2-x-3}|\underline{2x^2+1}$

            $\underline{4x^4-6x^2}$

                      $2x^2-x-3$                      (After subtraction)

                      $\underline{2x^2\quad \quad -3}$

                          $\underline{\quad -x\quad}$                        (After subtraction)

Now,

$\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}$

Therefore, the required solution is $2x^2+1-\dfrac{x}{2x^2-3}$.