document.write( "Question 124314: Find two numbers whose product is 48 and sum is 14?
\n" ); document.write( "2. Product -72 Sum -21 \n" ); document.write( "

Algebra.Com's Answer #91108 by jim_thompson5910(35256) $\"\"$ $\"About$

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# 1\r
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\n" ); document.write( "\n" ); document.write( "Let's list all of the factors of 48:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 48:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,48\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...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 48\r
\n" ); document.write( "\n" ); document.write( "1*48\r
\n" ); document.write( "\n" ); document.write( "2*24\r
\n" ); document.write( "\n" ); document.write( "3*16\r
\n" ); document.write( "\n" ); document.write( "4*12\r
\n" ); document.write( "\n" ); document.write( "6*8\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-8)\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 14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 14\r
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First Number	Second Number	Sum
1	48	1+48=49
2	24	2+24=26
3	16	3+16=19
4	12	4+12=16
6	8	6+8=14
-1	-48	-1+(-48)=-49
-2	-24	-2+(-24)=-26
-3	-16	-3+(-16)=-19
-4	-12	-4+(-12)=-16
-6	-8	-6+(-8)=-14

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 6 and 8 add up to 14 and multiply to 48\r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( "Let's list all of the factors of -72:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -72:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,9,12,18,24,36,72\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-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 -72\r
\n" ); document.write( "\n" ); document.write( "(1)*(-72)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(8)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(72)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(36)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(18)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(9)\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 -21? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -21\r
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First Number	Second Number	Sum
1	-72	1+(-72)=-71
2	-36	2+(-36)=-34
3	-24	3+(-24)=-21
4	-18	4+(-18)=-14
6	-12	6+(-12)=-6
8	-9	8+(-9)=-1
-1	72	-1+72=71
-2	36	-2+36=34
-3	24	-3+24=21
-4	18	-4+18=14
-6	12	-6+12=6
-8	9	-8+9=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 3 and -24 add up to -21 and multiply to -72\r
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