Exemplo 2
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Exemplo 2
Determine o quociente, $q(x)$, e o resto, $r(x)$, da divisão de $p(x)=x^5+4x^2-2$ por $d(x)=x^2+2$.
| $x^5+0x^4+0x^3+4x^2+0x-2$ | $x^2+2$ |
| $-x^5+0x^4-2x^3+0x^2+0x+0$ | $x^3-2x+4$ |
| $-2x^3+4x^2+0x+0$ | |
| $+2x^3+0x^2+4x+0$ | |
| $4x^2+4x-2$ | |
| $-4x^2+0x-8$ | |
| $4x-10$ |
Então, $$p(x)=q(x) \times d(x) + r(x) \, \Leftrightarrow \, x^5+4x^2-2=(x^3-2x+4)(x^2+2)+(4x-10)$$
