<PRE><B>Question 915747</B>
I think you meant to say &quot;x-7&quot; instead of &quot;x+7&quot;


Looking at the expression {{{x^2+x-56}}}, we can see that the first coefficient is {{{1}}}, the second coefficient is {{{1}}}, and the last term is {{{-56}}}.



Now multiply the first coefficient {{{1}}} by the last term {{{-56}}} to get {{{(1)(-56)=-56}}}.



Now the question is: what two whole numbers multiply to {{{-56}}} (the previous product) &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to the second coefficient {{{1}}}?



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 {{{-56}}} (the previous product).



Factors of {{{-56}}}:

1,2,4,7,8,14,28,56

-1,-2,-4,-7,-8,-14,-28,-56



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to {{{-56}}}.

1*(-56) = -56
2*(-28) = -56
4*(-14) = -56
7*(-8) = -56
(-1)*(56) = -56
(-2)*(28) = -56
(-4)*(14) = -56
(-7)*(8) = -56


Now let&#39;s add up each pair of factors to see if one pair adds to the middle coefficient {{{1}}}:



&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;-56&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1+(-56)=-55&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-28&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;2+(-28)=-26&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-14&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;4+(-14)=-10&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;7&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-8&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;7+(-8)=-1&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;56&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-1+56=55&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;28&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-2+28=26&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;14&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-4+14=10&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;-7&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;8&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;-7+8=1&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From the table, we can see that the two numbers {{{-7}}} and {{{8}}} add to {{{1}}} (the middle coefficient).



So the two numbers {{{-7}}} and {{{8}}} both multiply to {{{-56}}} &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to {{{1}}}



Now replace the middle term {{{1x}}} with {{{-7x+8x}}}. Remember, {{{-7}}} and {{{8}}} add to {{{1}}}. So this shows us that {{{-7x+8x=1x}}}.



{{{x^2+highlight(-7x+8x)-56}}} Replace the second term {{{1x}}} with {{{-7x+8x}}}.



{{{(x^2-7x)+(8x-56)}}} Group the terms into two pairs.



{{{x(x-7)+(8x-56)}}} Factor out the GCF {{{x}}} from the first group.



{{{x(x-7)+8(x-7)}}} Factor out {{{8}}} 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.



{{{(x+8)(x-7)}}} Combine like terms. Or factor out the common term {{{x-7}}}



===============================================================



Answer:



So {{{x^2+x-56}}} factors to {{{(x+8)(x-7)}}}.



In other words, {{{x^2+x-56=(x+8)(x-7)}}}.



Note: you can check the answer by expanding {{{(x+8)(x-7)}}} to get {{{x^2+x-56}}} or by graphing the original expression and the answer (the two graphs should be identical).



Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at &lt;a href=&quot;mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help&quot;&gt;jim_thompson5910@hotmail.com&lt;/a&gt;
or you can visit my website here: &lt;a href=&quot;http://www.freewebs.com/jimthompson5910/home.html&quot;&gt;http://www.freewebs.com/jimthompson5910/home.html&lt;/a&gt;


Thanks,


Jim </PRE>