Given:
Division problem:
[tex](4x^4-4x^2-x-3)\div (2x^2-3)[/tex]
To find:
The solution for the given division problem.
Solution:
We have,
[tex](4x^4-4x^2-x-3)\div (2x^2-3)[/tex]
Here, 4x^4-4x^2-x-3 is the dividend and (2x^2-3) is divisor.
Using the long division method we get
[tex]\underline{2x^2-3}|\overline{4x^4-4x^2-x-3}|\underline{2x^2+1}[/tex]
[tex]\underline{4x^4-6x^2}[/tex]
[tex]2x^2-x-3[/tex] (After subtraction)
[tex]\underline{2x^2\quad \quad -3}[/tex]
[tex]\underline{\quad -x\quad}[/tex] (After subtraction)
Now,
[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Therefore, the required solution is [tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex].
