<PRE><B>Question 159301</B>
I&#39;m assuming you want to factor these? I&#39;ll do the first one to get you started





Looking at the expression {{{y^2-5y+4}}}, we can see that the first coefficient is {{{1}}}, the second coefficient is {{{-5}}}, and the last term is {{{4}}}.



Now multiply the first coefficient {{{1}}} by the last term {{{4}}} to get {{{(1)(4)=4}}}.



Now the question is: what two whole numbers multiply to {{{4}}} (the previous product) &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to the second coefficient {{{-5}}}?



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 {{{4}}} (the previous product).



Factors of {{{4}}}:

1,2,4

-1,-2,-4



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to {{{4}}}.

1*4
2*2
(-1)*(-4)
(-2)*(-2)


Now let&#39;s add up each pair of factors to see if one pair adds to the middle coefficient {{{-5}}}:



&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;4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;1+4=5&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;2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;2+2=4&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;-4&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=red&gt;-1+(-4)=-5&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;-2&lt;/font&gt;&lt;/td&gt;&lt;td  align=&quot;center&quot;&gt;&lt;font color=black&gt;-2+(-2)=-4&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;



From the table, we can see that the two numbers {{{-1}}} and {{{-4}}} add to {{{-5}}} (the middle coefficient).



So the two numbers {{{-1}}} and {{{-4}}} both multiply to {{{4}}} &lt;font size=4&gt;&lt;b&gt;and&lt;/b&gt;&lt;/font&gt; add to {{{-5}}}



Now replace the middle term {{{-5y}}} with {{{-y-4y}}}. Remember, {{{-1}}} and {{{-4}}} add to {{{-5}}}. So this shows us that {{{-y-4y=-5y}}}.



{{{y^2+highlight(-y-4y)+4}}} Replace the second term {{{-5y}}} with {{{-y-4y}}}.



{{{(y^2-y)+(-4y+4)}}} Group the terms into two pairs.



{{{y(y-1)+(-4y+4)}}} Factor out the GCF {{{y}}} from the first group.



{{{y(y-1)-4(y-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.



{{{(y-4)(y-1)}}} Combine like terms. Or factor out the common term {{{y-1}}}


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Answer:



So {{{y^2-5y+4}}} factors to {{{(y-4)(y-1)}}}.



Note: you can check the answer by FOILing {{{(y-4)(y-1)}}} to get {{{y^2-5y+4}}} or by graphing the original expression and the answer (the two graphs should be identical).
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