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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Teoremas de Resto e de Fator


Estudo e aplica\303\247\303\243o dos teoremas de resto e de fator.

[Instru\303\247\303\265es : Execute primeiramente a se\303\247\303\243o de recursos de c\303\263digos. Embora nenhum resultado seja apresentado imediatamente, essas defini\303\247\303\265es ser\303\243o usadas posteriormente nesta \303\241rea de trabalho.]

  0. C\303\263digo
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" 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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">  1. O Teorema do Resto


Uma vers\303\243o do teorema do resto \303\251 essa :

      Para um polin\303\264mio f(x), os seguintes s\303\243o equivalentes:
        - f(r) = R
        - O resto, quando  (x-r) \303\251 divididopor  f(x) \303\251 R

Isso faz uma conex\303\243o entre o resto de uma divis\303\243o de polin\303\264mios e a avalia\303\247\303\243o de um polin\303\264mio. Vejamos alguns exemplos.

Exemplo 1.1 :  Vamos criar um polin\303\264mio e escolher um n\303\272mero  r. ent\303\243o vamos calcular as duas express\303\265es acima e constatar que as duas s\303\243o a mesma.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Exemplo 1.2 :   Vejamos outro exemplo.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L17" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L18" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInJGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInJGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L19" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Group view="presentation" inline-output="false" labelreference="L21" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Exemplo 1.3 :  Este \303\251 um exemplo mais dif\303\255cil.</Font></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L22" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoZio2I0kieEdGKEYoNiRJKW9wZXJhdG9yR0YoSSZhcnJvd0dGKEYoLDIqJDkkIiIoIiIiKiRGNiIiJyEiIiokRjYiIiYiIiUqJEY2Rj4hIioqJEY2IiIkIiM2KiRGNiIiI0Y6RjYhIzciJFciRjhGKEYoRig3I0Yu</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJyR0YoIyEiKCIiIzcjRi4=</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInJGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInJGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEoMTUyNzc3N0YnRi8tRko2JFEkMTI4RidGLy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGVS8lKWJldmVsbGVkR0Y0Ri8=">IyEoeHhfIiIkRyI=</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L26" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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Em todos esses casos, voc\303\252 pode ver que o n\303\272mero obtido pelo c\303\241lculo do polin\303\264mio \303\251 o mesmo que o resto.
 
  2. O Teorema do Fator


O teorema do fator \303\251 uma conseq\303\274\303\252ncia do teorema do resto :

      Para um polin\303\264mio f(x), os seguintes s\303\243o equivalentes:
        - f(r) = 0
        - (x-r) divide f(x)
        - r \303\251 uma raiz de f(x)
        - o gr\303\241fico def(x) tem uma interse\303\247\303\243o de x em  x = r
     

Este teorema faz uma conex\303\243o entre as ra\303\255zes de um polin\303\264mio e fatores lineares. Vejamos na pr\303\241tica.
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<Input><Text-field style="Text" layout="Normal">Exemplo 2.1 :  </Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Esse polin\303\264mio tem tr\303\252s ra\303\255zes. Podemos esperar tr\303\252s fatores linares.....</Font></Text-field>
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Sempre que temos uma raiz, temos um fator linear, e logo temos como decompor o polin\303\264mio em um produto de polin\303\264mios  de grau menor.
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