What is (x^4-3x^2-4)/(x-2) ?

The solution to (x^4-3x^2-4)/(x-2) is (x^2+1)(x+2)

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simplify (x^4-3x^2-4)/(x-2)

simplify

\frac{x ^{4} - 3 x ^{2} - 4}{x - 2}

(x^{2} + 1) (x + 2)

Solution steps

\frac{x ^{4} - 3 x ^{2} - 4}{x - 2}

Let

u = x^{2}

= \frac{u ^{2} - 3 u - 4}{x - 2}

Factor

u^{2} - 3 u - 4 : (u + 1) (u - 4)

= \frac{( u + 1 ) ( u - 4 )}{x - 2}

Substitute back

u = x^{2}

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

Factor

x^{2} - 4 : (x + 2) (x - 2)

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

Cancel the common factor:

x - 2

= (x^{2} + 1) (x + 2)

(- 2 + 4 i) - (3 - 5 i)

3 x^{2} - x + 2 - 5 x^{2} + 8 x - 5

10 - 4 (2 x + 7)

- 3 \cdot 10

2 x + 5 - \frac{25}{1 - 2 x}