document.write( "Question 181957: 46. Factor completely. -3t^3+ 3t^2-6t\r
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\n" ); document.write( "\n" ); document.write( "60. Factor polynomial completely. 10a^2+ab-2b^2\r
\n" ); document.write( "\n" ); document.write( "80. Factor completely. 4m^2+20m+25\r
\n" ); document.write( "\n" ); document.write( "90. Factor each polynomial completely, given that the binomial Following it is a factor of the polynomial. x^3-4x^2-3x-10, x-5\r
\n" ); document.write( "\n" ); document.write( "102. Solve each equation. t2+1=13/6t
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Algebra.Com's Answer #136578 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first three to get you started:\r
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\n" ); document.write( "\n" ); document.write( "# 46\r
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\n" ); document.write( "\n" ); document.write( " $\"-3t%5E3%2B3t%5E2-6t\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"-3t%28t%5E2-t%2B2%29\"$ Factor out the GCF $\"-3t\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"-3t%5E3%2B3t%5E2-6t\"$ factors to $\"-3t%28t%5E2-t%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 60\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"10a%5E2%2Bab-2b%5E2\"$ we can see that the first term is $\"10a%5E2\"$ and the last term is $\"-2b%5E2\"$ where the coefficients are 10 and -2 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 10 and the last coefficient -2 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient 1? Let's list all of the factors of -20:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -20:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20 ...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 -20\r
\n" ); document.write( "\n" ); document.write( "(1)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-5)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(10)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(5)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1\r
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First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -4 and 5 add up to 1 and multiply to -20\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"10a%5E2%2Bab-2b%5E2\"$ , replace $\"ab\"$ with $\"-4ab%2B5ab\"$ (notice $\"-4ab%2B5ab\"$ adds up to $\"ab\"$ . So it is equivalent to $\"ab\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"10a%5E2%2Bhighlight%28-4ab%2B5ab%29%2B-2b%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"10a%5E2-4ab%2B5ab-2b%5E2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2810a%5E2-4ab%29%2B%285ab-2b%5E2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"2a%285a-2b%29%2Bb%285a-2b%29\"$ Factor out the GCF of $\"2a\"$ out of the first group. Factor out the GCF of $\"b\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%282a%2Bb%29%285a-2b%29\"$ Since we have a common term of $\"5a-2b\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"10a%5E2-4ab%2B5ab-2b%5E2\"$ factors to $\"%282a%2Bb%29%285a-2b%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"10a%5E2%2Bab-2b%5E2\"$ factors to $\"%282a%2Bb%29%285a-2b%29\"$ (since $\"10a%5E2%2Bab-2b%5E2\"$ is equivalent to $\"10a%5E2-4ab%2B5ab-2b%5E2\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"10a%5E2%2Bab-2b%5E2\"$ factors to $\"%282a%2Bb%29%285a-2b%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 80\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"4m%5E2%2B20m%2B25\"$ we can see that the first term is $\"4m%5E2\"$ and the last term is $\"25\"$ where the coefficients are 4 and 25 respectively.\r
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\n" ); document.write( "\n" ); document.write( "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 20? Let's list all of the factors of 100:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 100:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20,25,50\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20,-25,-50 ...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 100\r
\n" ); document.write( "\n" ); document.write( "1*100\r
\n" ); document.write( "\n" ); document.write( "2*50\r
\n" ); document.write( "\n" ); document.write( "4*25\r
\n" ); document.write( "\n" ); document.write( "5*20\r
\n" ); document.write( "\n" ); document.write( "10*10\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-100)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-50)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-25)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(-10)*(-10)\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 20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 20\r
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First Number	Second Number	Sum
1	100	1+100=101
2	50	2+50=52
4	25	4+25=29
5	20	5+20=25
10	10	10+10=20
-1	-100	-1+(-100)=-101
-2	-50	-2+(-50)=-52
-4	-25	-4+(-25)=-29
-5	-20	-5+(-20)=-25
-10	-10	-10+(-10)=-20

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 10 and 10 add up to 20 and multiply to 100\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"4m%5E2%2B20m%2B25\"$ , replace $\"20m\"$ with $\"10m%2B10m\"$ (notice $\"10m%2B10m\"$ adds up to $\"20m\"$ . So it is equivalent to $\"20m\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"4m%5E2%2Bhighlight%2810m%2B10m%29%2B25\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"4m%5E2%2B10m%2B10m%2B25\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%284m%5E2%2B10m%29%2B%2810m%2B25%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"2m%282m%2B5%29%2B5%282m%2B5%29\"$ Factor out the GCF of $\"2m\"$ out of the first group. Factor out the GCF of $\"5\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%282m%2B5%29%282m%2B5%29\"$ Since we have a common term of $\"2m%2B5\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"4m%5E2%2B10m%2B10m%2B25\"$ factors to $\"%282m%2B5%29%282m%2B5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"4m%5E2%2B20m%2B25\"$ factors to $\"%282m%2B5%29%282m%2B5%29\"$ (since $\"4m%5E2%2B20m%2B25\"$ is equivalent to $\"4m%5E2%2B10m%2B10m%2B25\"$ )\r
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\n" ); document.write( "\n" ); document.write( "note: $\"%282m%2B5%29%282m%2B5%29\"$ is equivalent to $\"%282m%2B5%29%5E2\"$ since the term $\"2m%2B5\"$ occurs twice. So $\"4m%5E2%2B20m%2B25\"$ also factors to $\"%282m%2B5%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"4m%5E2%2B20m%2B25\"$ factors to $\"%282m%2B5%29%5E2\"$ \r
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