document.write( "Question 405579: Can someone please help me? \r
\n" ); document.write( "\n" ); document.write( "Factor and show work, If prime state this.\r
\n" ); document.write( "\n" ); document.write( "144-25t+t^2 \n" ); document.write( "

Algebra.Com's Answer #286453 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Rearrange the terms to get $\"t%5E2-25t%2B144\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"t%5E2-25t%2B144\"$ we can see that the first term is $\"t%5E2\"$ and the last term is $\"144\"$ where the coefficients are 1 and 144 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 144 to get 144. Now what two numbers multiply to 144 and add to the middle coefficient -25? Let's list all of the factors of 144:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 144:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,9,12,16,18,24,36,48,72\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to 144\r
\n" ); document.write( "\n" ); document.write( "1*144\r
\n" ); document.write( "\n" ); document.write( "2*72\r
\n" ); document.write( "\n" ); document.write( "3*48\r
\n" ); document.write( "\n" ); document.write( "4*36\r
\n" ); document.write( "\n" ); document.write( "6*24\r
\n" ); document.write( "\n" ); document.write( "8*18\r
\n" ); document.write( "\n" ); document.write( "9*16\r
\n" ); document.write( "\n" ); document.write( "12*12\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-144)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-72)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(-9)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-12)*(-12)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "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\r
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First Number	Second Number	Sum
1	144	1+144=145
2	72	2+72=74
3	48	3+48=51
4	36	4+36=40
6	24	6+24=30
8	18	8+18=26
9	16	9+16=25
12	12	12+12=24
-1	-144	-1+(-144)=-145
-2	-72	-2+(-72)=-74
-3	-48	-3+(-48)=-51
-4	-36	-4+(-36)=-40
-6	-24	-6+(-24)=-30
-8	-18	-8+(-18)=-26
-9	-16	-9+(-16)=-25
-12	-12	-12+(-12)=-24

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -9 and -16 add up to -25 and multiply to 144\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"t%5E2-25t%2B144\"$ , replace $\"-25t\"$ with $\"-9t-16t\"$ (notice $\"-9t-16t\"$ adds up to $\"-25t\"$ . So it is equivalent to $\"-25t\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"t%5E2%2Bhighlight%28-9t-16t%29%2B144\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"t%5E2-9t-16t%2B144\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28t%5E2-9t%29%2B%28-16t%2B144%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"t%28t-9%29-16%28t-9%29\"$ Factor out the GCF of $\"t\"$ out of the first group. Factor out the GCF of $\"-16\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28t-16%29%28t-9%29\"$ Since we have a common term of $\"t-9\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"t%5E2-9t-16t%2B144\"$ factors to $\"%28t-16%29%28t-9%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"t%5E2-25t%2B144\"$ factors to $\"%28t-16%29%28t-9%29\"$ (since $\"t%5E2-25t%2B144\"$ is equivalent to $\"t%5E2-9t-16t%2B144\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"t%5E2-25t%2B144\"$ factors to $\"%28t-16%29%28t-9%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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