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Division of a Polynomial by a Polynomial

Perform the d...

Question

Perform the division $\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)}$ .

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Solution

$\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)} = \frac{(x^{4} + 3 x^{2} + 2)}{(x^{4} + 7 x^{2} + 12)}$

$x^{4} + 7 x^{2} + 12) x^{4} + 3 x^{2} + 2 (1$
$x^{4} + 7 x^{2} + 12$
$- - - - - -$
$- 4 x^{2} - 10$

$Q u o t i e n t = 1$

$R e m a i n d e r = - 4 x^{2} - 10$

$∴ \frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)} = 1 + \frac{(- 4 x^{2} - 10)}{x^{4} + 7 x^{2} + 12}$

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Similar questions

\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)} =

Q. Integrate the given equation

\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)}

Q. Integrate the rational function

\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)}

\int \frac{(x^{2} + 1) (x^{2} + 4)}{(x^{2} + 3) (x^{2} - 5)} d x

Q. Reduce to its simplest form:

\frac{(x^{2} + 1) (x^{2} + 2)}{(x^{2} + 3) (x^{2} + 4)}

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