document.write( "Question 326194: Sove using factoring and principle of zero products. Must show all work. (please explain how you did this so I can try to understand) Thank you in advance:
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Algebra.Com's Answer #233521 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2x%5E2%2Bx\"$ $\"%22%22=%22%22\"$ $\"42%2B9x\"$
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document.write( "The other tutor's solution is correct; however there is one step\r\n" );
document.write( "he did not do, which would have made the factoring easier.\r\n" );
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document.write( "Get a zero on the right by adding  to both sides\r\n" );
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document.write( "Combine like terms and simplify:\r\n" );
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document.write( "Since all the numbers are even we can divide every term by \r\n" );
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document.write( "[That is the step which the other tutor did not do, which makes it easier\r\n" );
document.write( "to factor.]\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "We must factor that.\r\n" );
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document.write( "I did some coloring so I can refer to the parts:\r\n" );
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document.write( "List all the ways to factor the red number 21 using two factors,\r\n" );
document.write( "(list the larger factor first):\r\n" );
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document.write( "Notice that the red sign (the one just before the 21 is \r\n" );
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document.write( "Put that sign between those numbers above instead of the multiplication \r\n" );
document.write( "sign, and give the answer:\r\n" );
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document.write( "Notice that the  is the same as the middle coefficient\r\n" );
document.write( "ignoring the sign: \r\n" );
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document.write( "Therefore write this:\r\n" );
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document.write( "Finally we put the signs in.  7 is the larger factor, and the red\r\n" );
document.write( "sign (the sign before the  is  in this:\r\n" );
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document.write( "So we place that sign before the 7\r\n" );
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document.write( "Next we place whichever sign before the 3 which will cause the product\r\n" );
document.write( "to come out to be , the last term of \r\n" );
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document.write( "That sign would have to be , so we have\r\n" );
document.write( "now completely factored the left side:\r\n" );
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document.write( "Next we use the zero-factor principle.\r\n" );
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document.write( "Each of the factors  and  represents some number.  \r\n" );
document.write( "Since their product must equal to 0,\r\n" );
document.write( "it is obvious that one of them is equal to 0.  But which one?\r\n" );
document.write( "We cannot tell, so it would be correct if  were\r\n" );
document.write( "0 and  something else. OR, it would also\r\n" );
document.write( "be correct if  were 0 and  were something else. \r\n" );
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document.write( "That's why there are two solutions to a quadratic equation. So we\r\n" );
document.write( "have to consider both possibilities:\r\n" );
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document.write( " OR \r\n" );
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document.write( "Solvving those we have two possibilities for solutions:\r\n" );
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document.write( " OR \r\n" );
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document.write( "Edwin

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