<PRE><B>Question 530186</B>
you mean factor a^2 - 2a - 15 ?






Looking at the expression {{{a^2-2a-15}}}, we can see that the first coefficient is {{{1}}}, the second coefficient is {{{-2}}}, and the last term is {{{-15}}}.



Now multiply the first coefficient {{{1}}} by the last term {{{-15}}} to get {{{(1)(-15)=-15}}}.



Now the question is: what two whole numbers multiply to {{{-15}}} (the previous product) &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to the second coefficient {{{-2}}}?



To find these two numbers, we need to list &lt;font size=4&gt;&lt;b&gt;all&lt;/b&gt;&lt;/font&gt; of the factors of {{{-15}}} (the previous product).



Factors of {{{-15}}}:

1,3,5,15

-1,-3,-5,-15



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to {{{-15}}}.

1*(-15) = -15
3*(-5) = -15
(-1)*(15) = -15
(-3)*(5) = -15


Now let&#39;s add up each pair of factors to see if one pair adds to the middle coefficient {{{-2}}}:



&lt;table border=&quot;1&quot;&gt;&lt;th&gt;First Number&lt;/th&gt;&lt;th&gt;Second Number&lt;/th&gt;&lt;th&gt;Sum&lt;/th&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-15&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1+(-15)=-14&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;3&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;-5&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;3+(-5)=-2&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-1&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;15&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-1+15=14&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-3&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;5&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-3+5=2&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From the table, we can see that the two numbers {{{3}}} and {{{-5}}} add to {{{-2}}} (the middle coefficient).



So the two numbers {{{3}}} and {{{-5}}} both multiply to {{{-15}}} &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to {{{-2}}}



Now replace the middle term {{{-2a}}} with {{{3a-5a}}}. Remember, {{{3}}} and {{{-5}}} add to {{{-2}}}. So this shows us that {{{3a-5a=-2a}}}.



{{{a^2+highlight(3a-5a)-15}}} Replace the second term {{{-2a}}} with {{{3a-5a}}}.



{{{(a^2+3a)+(-5a-15)}}} Group the terms into two pairs.



{{{a(a+3)+(-5a-15)}}} Factor out the GCF {{{a}}} from the first group.



{{{a(a+3)-5(a+3)}}} Factor out {{{5}}} from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



{{{(a-5)(a+3)}}} Combine like terms. Or factor out the common term {{{a+3}}}



===============================================================



Answer:



So {{{a^2-2a-15}}} factors to {{{(a-5)(a+3)}}}.



In other words, {{{a^2-2a-15=(a-5)(a+3)}}}.



Note: you can check the answer by expanding {{{(a-5)(a+3)}}} to get {{{a^2-2a-15}}} or by graphing the original expression and the answer (the two graphs should be identical).



If you need more help, email me at &lt;a href=&quot;mailto:jim_thompson5910@hotmail.com&quot;&gt;jim_thompson5910@hotmail.com&lt;/a&gt;


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Jim
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