<PRE><B>Question 787996</B>


Looking at the expression {{{2m^2-9m+4}}}, we can see that the first coefficient is {{{2}}}, the second coefficient is {{{-9}}}, and the last term is {{{4}}}.



Now multiply the first coefficient {{{2}}} by the last term {{{4}}} to get {{{(2)(4)=8}}}.



Now the question is: what two whole numbers multiply to {{{8}}} (the previous product) &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to the second coefficient {{{-9}}}?



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 {{{8}}} (the previous product).



Factors of {{{8}}}:

1,2,4,8

-1,-2,-4,-8



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to {{{8}}}.

1*8 = 8
2*4 = 8
(-1)*(-8) = 8
(-2)*(-4) = 8


Now let&#39;s add up each pair of factors to see if one pair adds to the middle coefficient {{{-9}}}:



&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;8&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1+8=9&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;4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;2+4=6&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;-1&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;-1+(-8)=-9&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;-4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-2+(-4)=-6&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From the table, we can see that the two numbers {{{-1}}} and {{{-8}}} add to {{{-9}}} (the middle coefficient).



So the two numbers {{{-1}}} and {{{-8}}} both multiply to {{{8}}} &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to {{{-9}}}



Now replace the middle term {{{-9m}}} with {{{-m-8m}}}. Remember, {{{-1}}} and {{{-8}}} add to {{{-9}}}. So this shows us that {{{-m-8m=-9m}}}.



{{{2m^2+highlight(-m-8m)+4}}} Replace the second term {{{-9m}}} with {{{-m-8m}}}.



{{{(2m^2-m)+(-8m+4)}}} Group the terms into two pairs.



{{{m(2m-1)+(-8m+4)}}} Factor out the GCF {{{m}}} from the first group.



{{{m(2m-1)-4(2m-1)}}} Factor out {{{4}}} 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.



{{{(m-4)(2m-1)}}} Combine like terms. Or factor out the common term {{{2m-1}}}



===============================================================



Answer:



So {{{2m^2-9m+4}}} factors to {{{(m-4)(2m-1)}}}.



In other words, {{{2m^2-9m+4=(m-4)(2m-1)}}}.



Note: you can check the answer by expanding {{{(m-4)(2m-1)}}} to get {{{2m^2-9m+4}}} or by graphing the original expression and the answer (the two graphs should be identical).
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