<PRE><B>Question 366639</B>
Looking at {{{10r^2-25r-6}}} we can see that the first term is {{{10r^2}}} and the last term is {{{-6}}} where the coefficients are 10 and -6 respectively.


Now multiply the first coefficient 10 and the last coefficient -6 to get -60. Now what two numbers multiply to -60 and add to the  middle coefficient -25? Let&#39;s list all of the factors of -60:




Factors of -60:

1,2,3,4,5,6,10,12,15,20,30,60


-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -60

(1)*(-60)

(2)*(-30)

(3)*(-20)

(4)*(-15)

(5)*(-12)

(6)*(-10)

(-1)*(60)

(-2)*(30)

(-3)*(20)

(-4)*(15)

(-5)*(12)

(-6)*(10)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to -25? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -25


&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;-60&lt;/td&gt;&lt;td&gt;1+(-60)=-59&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;-30&lt;/td&gt;&lt;td&gt;2+(-30)=-28&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;-20&lt;/td&gt;&lt;td&gt;3+(-20)=-17&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;-15&lt;/td&gt;&lt;td&gt;4+(-15)=-11&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;5&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;-12&lt;/td&gt;&lt;td&gt;5+(-12)=-7&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;-10&lt;/td&gt;&lt;td&gt;6+(-10)=-4&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;60&lt;/td&gt;&lt;td&gt;-1+60=59&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;30&lt;/td&gt;&lt;td&gt;-2+30=28&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;20&lt;/td&gt;&lt;td&gt;-3+20=17&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;15&lt;/td&gt;&lt;td&gt;-4+15=11&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td align=&quot;center&quot;&gt;-5&lt;/td&gt;&lt;td align=&quot;center&quot;&gt;12&lt;/td&gt;&lt;td&gt;-5+12=7&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;10&lt;/td&gt;&lt;td&gt;-6+10=4&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



None of these pairs of factors add to -25. So the expression {{{10r^2-25r-6}}} cannot be factored

</PRE>