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<h1>
Learning techniques online - Training problem solving skills - algebraic equations
</h1>
This&#x00A0;&#x000D;page&#x00A0;&#x000D;was&#x00A0;&#x000D;created&#x00A0;&#x000D;by&#x00A0;&#x000D; <a href="../../fc44.htm" target="_parent">EMMentor_Algebra_Equations</a>
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These&#x00A0;&#x000D;pages&#x00A0;&#x000D;allow&#x00A0;&#x000D;you&#x00A0;&#x000D;to&#x00A0;&#x000D;try&#x00A0;&#x000D;15&#x00A0;&#x000D;learning&#x00A0;&#x000D;techniques&#x00A0;&#x000D;out&#x00A0;&#x000D;of&#x00A0;&#x000D;57&#x00A0;&#x000D;techniques&#x00A0;&#x000D;available&#x00A0;&#x000D;in&#x00A0;&#x000D;the&#x00A0;&#x000D;program&#x00A0;&#x000D;EMMentor.&#x00A0;&#x000D;Each&#x00A0;&#x000D;learning&#x00A0;&#x000D;technique&#x00A0;&#x000D;applies&#x00A0;&#x000D;to&#x00A0;&#x000D;the&#x00A0;&#x000D;solution&#x00A0;&#x000D;of&#x00A0;&#x000D;math&#x00A0;&#x000D;problem.&#x00A0;&#x000D;Select&#x00A0;&#x000D;a&#x00A0;&#x000D;technique&#x00A0;&#x000D;and&#x00A0;&#x000D;do&#x00A0;&#x000D;what&#x00A0;&#x000D;is&#x00A0;&#x000D;required&#x00A0;&#x000D;at&#x00A0;&#x000D;each&#x00A0;&#x000D;solution&#x00A0;&#x000D;step.&#x00A0;&#x000D;If&#x00A0;&#x000D;doubt,&#x00A0;&#x000D;click&#x00A0;&#x000D;an&#x00A0;&#x000D;arrow&#x00A0;&#x000D;and&#x00A0;&#x000D;get&#x00A0;&#x000D;this&#x00A0;&#x000D;step&#x00A0;&#x000D;done.&#x00A0;&#x000D;An&#x00A0;&#x000D;icon&#x00A0;&#x000D;of&#x00A0;&#x000D;magnifier&#x00A0;&#x000D;allows&#x00A0;&#x000D;seeing&#x00A0;&#x000D;all&#x00A0;&#x000D;steps&#x00A0;&#x000D;done.&#x00A0;&#x000D;All&#x00A0;&#x000D;examples&#x00A0;&#x000D;include&#x00A0;&#x000D;an&#x00A0;&#x000D;option&#x00A0;&#x000D;of&#x00A0;&#x000D;translation&#x00A0;&#x000D;to&#x00A0;&#x000D;German&#x00A0;&#x000D;(a&#x00A0;&#x000D;globe&#x00A0;&#x000D;icon).&#x00A0;&#x000D;The&#x00A0;&#x000D;program&#x00A0;&#x000D;EMMentor&#x00A0;&#x000D;offers&#x00A0;&#x000D;all&#x00A0;&#x000D;shown&#x00A0;&#x000D;learning&#x00A0;&#x000D;techniques.&#x00A0;&#x000D;The&#x00A0;&#x000D;first&#x00A0;&#x000D;two&#x00A0;&#x000D;learning&#x00A0;&#x000D;techniques&#x00A0;&#x000D;are&#x00A0;&#x000D;available&#x00A0;&#x000D;in&#x00A0;&#x000D;the&#x00A0;&#x000D;programs&#x00A0;&#x000D;EMSolution&#x00A0;&#x000D;and&#x00A0;&#x000D;EMMentor.&#x00A0;&#x000D;At&#x00A0;&#x000D;the&#x00A0;&#x000D;bottom&#x00A0;&#x000D;of&#x00A0;&#x000D;this&#x00A0;&#x000D;page&#x00A0;&#x000D;we&#x00A0;&#x000D;offer&#x00A0;&#x000D;you&#x00A0;&#x000D;to&#x00A0;&#x000D;see&#x00A0;&#x000D;examples&#x00A0;&#x000D;of&#x00A0;&#x000D;performance/error&#x00A0;&#x000D;analysis&#x00A0;&#x000D;available&#x00A0;&#x000D;in&#x00A0;&#x000D;the&#x00A0;&#x000D;program&#x00A0;&#x000D;EMMentor.&#x00A0;&#x000D;
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<table width="724" ><tr><td width="150"><a href="jawascript:void(0)" onClick="window.open('../../demo_method.htm','WindowName','width=750,height=650,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;"><b>Learning&#x00A0;&#x000D;techniques</b></a></td><td><table width="100%"><tr><td width="14" class="tabsheet1"><div align="center"><a href="../../method_7/base/v_0_0.xml" target="_parent"><b>1</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_7_a/base/v_0_0.xml" target="_parent"><b>2</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_7_b/base/v_0_0.xml" target="_parent"><b>3</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_10/base/v_0_1.xml" target="_parent"><b>4</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_11/base/v_0_1.xml" target="_parent"><b>5</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_12/base/v_0_1.xml" target="_parent"><b>6</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_13/base/v_0_1.xml" target="_parent"><b>7</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_14/base/v_0_1.xml" target="_parent"><b>8</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_32/base/v_0_1.xml" target="_parent"><b>9</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_33/base/v_0_1.xml" target="_parent"><b>10</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../Method_39/base/v_0_1.xml" target="_parent"><b>11</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_40/base/v_0_1.xml" target="_parent"><b>12</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_44/base/v_0_1.xml" target="_parent"><b>13</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_47/base/v_0_1.xml" target="_parent"><b>14</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_48/base/v_0_1.xml" target="_parent"><b>15</b></a></div></td><td width="14" class="tabsheet1"><div align="center"><a href="../../method_51/base/v_0_1.xml" target="_parent"><b><font color="FF9900">16</font></b></a></div></td></tr></table></td><td width="350" align="right"><div align="right"><b><font color="FF9900">Independent solving</font></b></div></td></tr></table>
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<b>Description</b>
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With&#x00A0;&#x000D;no&#x00A0;&#x000D;hints&#x00A0;&#x000D;available,&#x00A0;&#x000D;you&#x00A0;&#x000D;have&#x00A0;&#x000D;to&#x00A0;&#x000D;select&#x00A0;&#x000D;math&#x00A0;&#x000D;transformation&#x00A0;&#x000D;from&#x00A0;&#x000D;the&#x00A0;&#x000D;offered&#x00A0;&#x000D;list&#x00A0;&#x000D;for&#x00A0;&#x000D;each&#x00A0;&#x000D;step&#x00A0;&#x000D;of&#x00A0;&#x000D;solution.&#x00A0;&#x000D;This&#x00A0;&#x000D;algorithm&#x00A0;&#x000D;trains&#x00A0;&#x000D;active&#x00A0;&#x000D;problem-solving&#x00A0;&#x000D;and&#x00A0;&#x000D;reasoning&#x00A0;&#x000D;skills.
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<b>Rational equations</b><br></br>
<b>Algebraic high-power equations</b><br></br>
<b>High-degree equations. Grouping method</b><br></br>
<a name="pont0">
<b>Solve the equation</b>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><msup><mi>r</mi><mi>4</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi><msup><mi>r</mi><mi>3</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>14 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>30 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
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<p><a href="jawascript:void(0)" onClick="window.open('0_0_1.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;"><b>1</b></a>. By&#x00A0;&#x000D;adding&#x00A0;&#x000D;and&#x00A0;&#x000D;subtracting&#x00A0;&#x000D;the&#x00A0;&#x000D;same&#x00A0;&#x000D;addends,&#x00A0;&#x000D;let&#x00A0;&#x000D;us&#x00A0;&#x000D;convert&#x00A0;&#x000D;the&#x00A0;&#x000D;polynomial&#x00A0;&#x000D;of&#x00A0;&#x000D;the&#x00A0;&#x000D;fourth&#x00A0;&#x000D;degree&#x00A0;&#x000D;into&#x00A0;&#x000D;a&#x00A0;&#x000D;sum&#x00A0;&#x000D;of&#x00A0;&#x000D;three&#x00A0;&#x000D;polynomials</p>
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<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><msup><mi>r</mi><mi>4</mi></msup></mrow><mrow><mo>+</mo><mi>2 </mi><msup><mi>r</mi><mi>3</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>+</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>4 </mi><msup><mi>r</mi><mi>3</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>28 </mi><mi>r</mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>+</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>2 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<b>Methodical task:</b> 
Scheme "To solve independently 1"
<table>
<tr><td></td><td>
To select the transformation
</td></tr>
</table>
<p><b>Select the continuation</b></p>
<table>
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('answer.htm','WindowName','width=450,height=220,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td>
To factor the quadratic trinomial(s)
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<a href="v_0_2.xml#pont2" target="_self">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
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To factor the power argument and coefficient out of polynomial
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<td>
Solve the equation
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