document.write( "Question 151213This question is from textbook Intermediate Algebra
\n" ); document.write( ": I need help!!! I am suppose to describe a strategy for factoring a polynomial and give example showing all your steps. Can someone help me on this one. \n" ); document.write( "

Algebra.Com's Answer #111104 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "Let's say that we want to factor $\"4x%5E2-14x-30\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2-14x-30\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"2%282x%5E2-7x-15%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"2x%5E2-7x-15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2x%5E2-7x-15\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-7\"$ , and the last term is $\"-15\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"-15\"$ to get $\"%282%29%28-15%29=-30\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-30\"$ (the previous product) and add to the second coefficient $\"-7\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-30\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-30\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,5,6,10,15,30\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-5,-6,-10,-15,-30\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. 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 $\"-30\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-30)
\n" ); document.write( "2*(-15)
\n" ); document.write( "3*(-10)
\n" ); document.write( "5*(-6)
\n" ); document.write( "(-1)*(30)
\n" ); document.write( "(-2)*(15)
\n" ); document.write( "(-3)*(10)
\n" ); document.write( "(-5)*(6)\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-7\"$ :\r
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First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"3\"$ and $\"-10\"$ add to $\"-7\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"3\"$ and $\"-10\"$ both multiply to $\"-30\"$ and add to $\"-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-7x\"$ with $\"3x-10x\"$ . Remember, $\"3\"$ and $\"-10\"$ add to $\"-7\"$ . So this shows us that $\"3x-10x=-7x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%283x-10x%29-15\"$ Replace the second term $\"-7x\"$ with $\"3x-10x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2%2B3x%29%2B%28-10x-15%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x%2B3%29%2B%28-10x-15%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x%2B3%29-5%282x%2B3%29\"$ Factor out $\"5\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-5%29%282x%2B3%29\"$ Combine like terms. Or factor out the common term $\"2x%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"2%282x%5E2-7x-15%29\"$ factors down to $\"2%28x-5%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-14x-30\"$ factors to $\"2%28x-5%29%282x%2B3%29\"$ .\r
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