<PRE><B>Question 119774</B>
Do you want to factor?





Looking at {{{w^2+4w-84}}} we can see that the first term is {{{w^2}}} and the last term is {{{-84}}} where the coefficients are 1 and -84 respectively.


Now multiply the first coefficient 1 and the last coefficient -84 to get -84. Now what two numbers multiply to -84 and add to the  middle coefficient 4? Let&#39;s list all of the factors of -84:




Factors of -84:

1,2,3,4,6,7,12,14,21,28,42,84


-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -84

(1)*(-84)

(2)*(-42)

(3)*(-28)

(4)*(-21)

(6)*(-14)

(7)*(-12)

(-1)*(84)

(-2)*(42)

(-3)*(28)

(-4)*(21)

(-6)*(14)

(-7)*(12)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4


&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;1&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-84&lt;/td&gt;&lt;td&gt;1+(-84)=-83&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;2&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-42&lt;/td&gt;&lt;td&gt;2+(-42)=-40&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;3&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-28&lt;/td&gt;&lt;td&gt;3+(-28)=-25&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;4&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-21&lt;/td&gt;&lt;td&gt;4+(-21)=-17&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;6&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-14&lt;/td&gt;&lt;td&gt;6+(-14)=-8&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;7&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-12&lt;/td&gt;&lt;td&gt;7+(-12)=-5&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-1&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;84&lt;/td&gt;&lt;td&gt;-1+84=83&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-2&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;42&lt;/td&gt;&lt;td&gt;-2+42=40&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-3&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;28&lt;/td&gt;&lt;td&gt;-3+28=25&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-4&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;21&lt;/td&gt;&lt;td&gt;-4+21=17&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-6&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;14&lt;/td&gt;&lt;td&gt;-6+14=8&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-7&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;12&lt;/td&gt;&lt;td&gt;-7+12=5&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;

None of these pairs of factors add to 4. So the expression {{{w^2+4w-84}}} cannot be factored

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