document.write( "Question 144991: The polynomial (x - 2) is a factor of the polynomial F(x) = 3x^2 - 8x + 2.
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Algebra.Com's Answer #105671 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First let's factor $\"3x%5E2-8x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"3x%5E2-8x%2B2\"$ we can see that the first term is $\"3x%5E2\"$ and the last term is $\"2\"$ where the coefficients are 3 and 2 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let's list all of the factors of 6:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 6:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6 ...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 6\r
\n" ); document.write( "\n" ); document.write( "1*6\r
\n" ); document.write( "\n" ); document.write( "2*3\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-3)\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 -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8\r
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First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

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\n" ); document.write( "\n" ); document.write( "None of these pairs of factors add to -8. So the expression $\"3x%5E2-8x%2B2\"$ cannot be factored\r
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\n" ); document.write( "\n" ); document.write( "So (x - 2) is NOT a factor of $\"3x%5E2-8x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the statement is false \n" ); document.write( "

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