document.write( "Question 116031: Hello,\r
\n" ); document.write( "\n" ); document.write( "Can someone please factor this completely.\r
\n" ); document.write( "\n" ); document.write( "-10w squared - 28w + 6 \n" ); document.write( "

Algebra.Com's Answer #84401 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"-10w%5E2-28w%2B6\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"-2%285w%5E2%2B14w-3%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"5w%5E2%2B14w-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"5w%5E2%2B14w-3\"$ we can see that the first term is $\"5w%5E2\"$ and the last term is $\"-3\"$ where the coefficients are 5 and -3 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 5 and the last coefficient -3 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 14? Let's list all of the factors of -15:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -15:\r
\n" ); document.write( "\n" ); document.write( "1,3,5,15\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-5,-15 ...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 -15\r
\n" ); document.write( "\n" ); document.write( "(1)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-5)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(15)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(5)\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 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	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -1 and 15 add up to 14 and multiply to -15\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"5w%5E2%2B14w-3\"$ , replace $\"14w\"$ with $\"-1w%2B15w\"$ (notice $\"-1w%2B15w\"$ adds up to $\"14w\"$ . So it is equivalent to $\"14w\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"5w%5E2%2Bhighlight%28-1w%2B15w%29%2B-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"5w%5E2-1w%2B15w-3\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%285w%5E2-1w%29%2B%2815w-3%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"w%285w-1%29%2B3%285w-1%29\"$ Factor out the GCF of $\"w\"$ out of the first group. Factor out the GCF of $\"3\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28w%2B3%29%285w-1%29\"$ Since we have a common term of $\"5w-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"5w%5E2-1w%2B15w-3\"$ factors to $\"%28w%2B3%29%285w-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"5w%5E2%2B14w-3\"$ factors to $\"%28w%2B3%29%285w-1%29\"$ (since $\"5w%5E2%2B14w-3\"$ is equivalent to $\"5w%5E2-1w%2B15w-3\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"-2%28w%2B3%29%285w-1%29\"$ Now reintroduce the GCF\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"-10w%5E2-28w%2B6\"$ factors to $\"-2%28w%2B3%29%285w-1%29\"$ \n" ); document.write( "

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