document.write( "Question 115073This question is from textbook Beginning algebra
\n" ); document.write( ": Factor the following trinomial completely\r
\n" ); document.write( "\n" ); document.write( "x squared -11x-60 \n" ); document.write( "

Algebra.Com's Answer #83705 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"x%5E2-11x-60\"$ we can see that the first term is $\"x%5E2\"$ and the last term is $\"-60\"$ where the coefficients are 1 and -60 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -60 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient -11? Let's list all of the factors of -60:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -60:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...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 -60\r
\n" ); document.write( "\n" ); document.write( "(1)*(-60)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-30)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(60)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(30)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(15)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(10)\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 -11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -11\r
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First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 4 and -15 add up to -11 and multiply to -60\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"x%5E2-11x-60\"$ , replace $\"-11x\"$ with $\"4x%2B-15x\"$ (notice $\"4x%2B-15x\"$ adds up to $\"-11x\"$ . So it is equivalent to $\"-11x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%284x%2B-15x%29%2B-60\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"x%5E2%2B4x-15x-60\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B4x%29%2B%28-15x-60%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29-15%28x%2B4%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-15\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-15%29%28x%2B4%29\"$ Since we have a common term of $\"x%2B4\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B4x-15x-60\"$ factors to $\"%28x-15%29%28x%2B4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"x%5E2-11x-60\"$ factors to $\"%28x-15%29%28x%2B4%29\"$ (since $\"x%5E2-11x-60\"$ is equivalent to $\"x%5E2%2B4x-15x-60\"$ )\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-11x-60\"$ factors to $\"%28x-15%29%28x%2B4%29\"$ \n" ); document.write( "

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