document.write( "Question 141506: Which of the following is another version of $\"f%28x%29+=+2x%5E2+-+4x+-+7\"$ ?
\n" ); document.write( "a. $\"f%28x%29+=+2%28x+-1%29%5E2+-+9\"$
\n" ); document.write( "b. $\"f%28x%29+=+%28x+-+1%29%5E2+-+9\"$
\n" ); document.write( "c. $\"f%28x%29+=+%28x+%2B+1%29%5E2+-+1%2F2\"$
\n" ); document.write( "d. $\"f%28x%29\"$ cannot be factored; prime \n" ); document.write( "

Algebra.Com's Answer #103112 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
Which of the following is another version of $\"f%28x%29+=+2x%5E2+-+4x+-+7\"$ ?
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\n" ); document.write( "b. $\"f%28x%29+=+%28x+-+1%29%5E2+-+9\"$
\n" ); document.write( "c. $\"f%28x%29+=+%28x+%2B+1%29%5E2+-+1%2F2\"$
\n" ); document.write( "d. $\"f%28x%29\"$ cannot be factored; prime
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document.write( "We can eliminate d because none of the choices are\r\n" );
document.write( "factorizations of f(x) anyway.\r\n" );
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document.write( "The easy way to find which one is correct is to substitute\r\n" );
document.write( "an arbitrary value for , ( is a good choice since it's easy)\r\n" );
document.write( "in the original and in each of the choices.\r\n" );
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document.write( "Substituting x=0 in the original:\r\n" );
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document.write( "Now substitute  in the answer a.\r\n" );
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document.write( "So a. is possible.\r\n" );
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document.write( "Now substitute  in the answer b.\r\n" );
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document.write( "So b. is NOT possible.\r\n" );
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document.write( "Now substitute  in the choice c.\r\n" );
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document.write( "So c. is NOT possible.\r\n" );
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document.write( "Thus the only possible choice is a.\r\n" );
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document.write( "However, that's not what your teacher wants you\r\n" );
document.write( "to do, although it is one way to get the correct\r\n" );
document.write( "answer on a multiple choice test. I just thought \r\n" );
document.write( "I'd show you the above method of substituting in\r\n" );
document.write( "each of the answers to rule out the incorrect \r\n" );
document.write( "choices. This may save you from having to miss a \r\n" );
document.write( "problem which you can't solve on a multiple \r\n" );
document.write( "choice test. Of course, this method will not work \r\n" );
document.write( "on the kind of test where you have to show your \r\n" );
document.write( "work.\r\n" );
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document.write( "Here is what your teacher wanted you to do:\r\n" );
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document.write( "Factor 2 out of the first two terms only:\r\n" );
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document.write( "We will complete the square inside the parentheses:\r\n" );
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document.write( "Multiply the coefficient of x, which is -2, by ,\r\n" );
document.write( "getting -1.  Then square -1 getting +1\r\n" );
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document.write( "So add +1 and immediately subtract 1 inside the \r\n" );
document.write( "parentheses:\r\n" );
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document.write( "Change the parentheses to brackets so they can hold \r\n" );
document.write( "parentheses:\r\n" );
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document.write( "[]\r\n" );
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document.write( "Factor only the first three terms inside the brackets:\r\n" );
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document.write( "Now remove the brackets by distributing the 2, leaving\r\n" );
document.write( "the  intact:\r\n" );
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document.write( "Combine the  and the  and get \r\n" );
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document.write( "which is choice a.\r\n" );
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document.write( "Edwin

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