document.write( "Question 77050This question is from textbook Glencoe Algebra 1
\n" ); document.write( ": \"%28x%2B1%29%28x%2B8%29=-12\" \n" ); document.write( "
Algebra.Com's Answer #55219 by jim_thompson5910(35256)\"\" \"About 
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\"%28x%2B1%29%28x%2B8%29=-12\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B9x%2B8=-12\" foil the left side\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B9x%2B20=0\" Add 12 to both sides\r
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B9%2Ax%2B20\", first we need to ask ourselves: What two numbers multiply to 20 and add to 9? Lets find out by listing all of the possible factors of 20
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,2,4,5,10,20,
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\n" ); document.write( " -1,-2,-4,-5,-10,-20,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to 20.
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\n" ); document.write( " 1*20=20
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\n" ); document.write( " 2*10=20
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\n" ); document.write( " 4*5=20
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\n" ); document.write( " (-1)*(-20)=20
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\n" ); document.write( " (-2)*(-10)=20
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\n" ); document.write( " (-4)*(-5)=20
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\n" ); document.write( " note: remember two negative numbers multiplied together make a positive number
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\n" ); document.write( " Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9
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First Number|Second Number|Sum
1|20|1+20=21
2|10|2+10=12
4|5|4+5=9
-1|-20|-1+(-20)=-21
-2|-10|-2+(-10)=-12
-4|-5|-4+(-5)=-9
We can see from the table that 4 and 5 add to 9. So the two numbers that multiply to 20 and add to 9 are: 4 and 5\r\n" ); document.write( " \r\n" ); document.write( " Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" ); document.write( " \r\n" ); document.write( " \"%28x%2Ba%29%28x%2Bb%29\"substitute a=4 and b=5\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x+4)(x+5)\r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x+4)(x+5) we get the quadratic \"1%2Ax%5E2%2B9%2Ax%2B20\" again\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "So the quadratic \"x%5E2%2B9x%2B20=0\" factors to
\n" ); document.write( "\"%28x%2B4%29%28x%2B5%29=0\"
\n" ); document.write( "Set each factor equal to zero
\n" ); document.write( "\"x%2B4=0\"
\n" ); document.write( "\"x=-4\"\r
\n" ); document.write( "\n" ); document.write( "\"x%2B5=0\"
\n" ); document.write( "\"x=-5\"
\n" ); document.write( "So our answer is
\n" ); document.write( "\"x=-4\" or \"x=-5\" \n" ); document.write( "
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