<PRE><B>Question 119713</B>


Looking at {{{4x^2-15x-25}}} we can see that the first term is {{{4x^2}}} and the last term is {{{-25}}} where the coefficients are 4 and -25 respectively.


Now multiply the first coefficient 4 and the last coefficient -25 to get -100. Now what two numbers multiply to -100 and add to the  middle coefficient -15? Let&#39;s list all of the factors of -100:




Factors of -100:

1,2,4,5,10,20,25,50


-1,-2,-4,-5,-10,-20,-25,-50 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -100

(1)*(-100)

(2)*(-50)

(4)*(-25)

(5)*(-20)

(-1)*(100)

(-2)*(50)

(-4)*(25)

(-5)*(20)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15


&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;-100&lt;/td&gt;&lt;td&gt;1+(-100)=-99&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;-50&lt;/td&gt;&lt;td&gt;2+(-50)=-48&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;-25&lt;/td&gt;&lt;td&gt;4+(-25)=-21&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;-20&lt;/td&gt;&lt;td&gt;5+(-20)=-15&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;100&lt;/td&gt;&lt;td&gt;-1+100=99&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;50&lt;/td&gt;&lt;td&gt;-2+50=48&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;25&lt;/td&gt;&lt;td&gt;-4+25=21&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;20&lt;/td&gt;&lt;td&gt;-5+20=15&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From this list we can see that 5 and -20 add up to -15 and multiply to -100



Now looking at the expression {{{4x^2-15x-25}}}, replace {{{-15x}}} with {{{5x+-20x}}} (notice {{{5x+-20x}}} adds up to {{{-15x}}}. So it is equivalent to {{{-15x}}})


{{{4x^2+highlight(5x+-20x)+-25}}}



Now let&#39;s factor {{{4x^2+5x-20x-25}}} by grouping:



{{{(4x^2+5x)+(-20x-25)}}} Group like terms



{{{x(4x+5)-5(4x+5)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{-5}}} out of the second group



{{{(x-5)(4x+5)}}} Since we have a common term of {{{4x+5}}}, we can combine like terms


So {{{4x^2+5x-20x-25}}} factors to {{{(x-5)(4x+5)}}}



So this also means that {{{4x^2-15x-25}}} factors to {{{(x-5)(4x+5)}}} (since {{{4x^2-15x-25}}} is equivalent to {{{4x^2+5x-20x-25}}})





So {{{4x^2-15x-25}}} factors to {{{(x-5)(4x+5)}}} 






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