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<title>A.II.3.18</title>
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<div class="feladat">
<b>Feladat: 3.18.</b><br /> <a name="a_ii_horner_100718_HP_03" /><a href="bib_box.php?mode=sne-s-j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num='); return false;"></a>Ellenőrizzük, hogy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>12</m:mn>

<m:msup><m:mrow><m:mi>x</m:mi></m:mrow><m:mrow><m:mn>4</m:mn></m:mrow>

</m:msup>

<m:mo>-</m:mo><m:mn>4</m:mn>

<m:msup><m:mrow><m:mi>x</m:mi></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

<m:mo>-</m:mo><m:mn>21</m:mn>

<m:msup><m:mrow><m:mi>x</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mo>-</m:mo><m:mn>2</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>3</m:mn></m:mrow></m:math> gyökei <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo>-</m:mo><m:mn>1</m:mn><m:mo>;</m:mo><m:mi>&ensp;</m:mi><m:mo>-</m:mo><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn><m:mo>;</m:mo><m:mi>&ensp;</m:mi><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>3</m:mn><m:mo>;</m:mo><m:mi>&ensp;</m:mi><m:mn>3</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn></m:mrow></m:math>.
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<div class="feladat">
<a name="_solution_a_ii_horner_100718_HP_03" /><b>Megoldás: 3.18</b><br />
A Horner-elrendezéses számolás eredménye:

<br />

<table width="100%"><tr><td align="center">

    <m:math xmlns="http://www.w3.org/1998/Math/MathML">

    <m:mstyle displaystyle="true"><m:mrow>

<m:mtable>

<m:mtr><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>4</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>21</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>2</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>16</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>5</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>0</m:mn></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>16</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>5</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>3</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>22</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>6</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>0</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>6</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>11</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>3</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>18</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>0</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>4</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mn>6</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>12</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>0</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow><m:mn>18</m:mn></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd><m:mtd columnalign="right"><m:mrow></m:mrow></m:mtd></m:mtr></m:mtable>

</m:mrow>

    </m:mstyle></m:math>

</td></tr></table>

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A polinom kapott szorzatalakja <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>12</m:mn><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>1</m:mn><m:mo stretchy="false">/</m:mo><m:mn>2</m:mn><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>1</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>.
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