Question

(4x⁴-4x²-x-3) ÷ (2x²-3)


so far i have 2x²+1+?/2x²-3
what is the question mark? ​

Answer 1

Answer:

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

Step-by-step explanation:

Use the long division method to divide polynomials:

$\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}$

Therefore:

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