<PRE><B>Question 374474</B>


{{{7x^6-63x^5+14x^4}}} Start with the given expression.



{{{7x^4(x^2-9x+2)}}} Factor out the GCF {{{7x^4}}}.



Now let&#39;s try to factor the inner expression {{{x^2-9x+2}}}



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Looking at the expression {{{x^2-9x+2}}}, we can see that the first coefficient is {{{1}}}, the second coefficient is {{{-9}}}, and the last term is {{{2}}}.



Now multiply the first coefficient {{{1}}} by the last term {{{2}}} to get {{{(1)(2)=2}}}.



Now the question is: what two whole numbers multiply to {{{2}}} (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 {{{2}}} (the previous product).



Factors of {{{2}}}:

1,2

-1,-2



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to {{{2}}}.

1*2 = 2
(-1)*(-2) = 2


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;2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1+2=3&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;-2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-1+(-2)=-3&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From the table, we can see that there are no pairs of numbers which add to {{{-9}}}. So {{{x^2-9x+2}}} cannot be factored.



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&lt;a name=&quot;ans&quot;&gt;


Answer:



So {{{7x^6-63x^5+14x^4}}} simply factors to {{{7x^4(x^2-9x+2)}}}



In other words, {{{7x^6-63x^5+14x^4=7x^4(x^2-9x+2)}}}.



If you need more help, email me at &lt;a href=&quot;mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help&quot;&gt;jim_thompson5910@hotmail.com&lt;/a&gt;


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Jim</PRE>