document.write( "Question 112297: What is the factored form of 4x^2+13-12? \n" ); document.write( "

Algebra.Com's Answer #81916 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"4x%5E2%2B13x-12\"$ we can see that the first term is $\"4x%5E2\"$ and the last term is $\"-12\"$ where the coefficients are 4 and -12 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 4 and the last coefficient -12 to get -48. Now what two numbers multiply to -48 and add to the middle coefficient 13? Let's list all of the factors of -48:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -48:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,48\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...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 -48\r
\n" ); document.write( "\n" ); document.write( "(1)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(48)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(16)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(8)\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 13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 13\r
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First Number	Second Number	Sum
1	-48	1+(-48)=-47
2	-24	2+(-24)=-22
3	-16	3+(-16)=-13
4	-12	4+(-12)=-8
6	-8	6+(-8)=-2
-1	48	-1+48=47
-2	24	-2+24=22
-3	16	-3+16=13
-4	12	-4+12=8
-6	8	-6+8=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -3 and 16 add up to 13 and multiply to -48\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"4x%5E2%2B13x-12\"$ , replace $\"13x\"$ with $\"-3x%2B16x\"$ (notice $\"-3x%2B16x\"$ adds up to $\"13x\"$ . So it is equivalent to $\"13x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%2Bhighlight%28-3x%2B16x%29%2B-12\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"4x%5E2-3x%2B16x-12\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%5E2-3x%29%2B%2816x-12%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%284x-3%29%2B4%284x-3%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"4\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B4%29%284x-3%29\"$ Since we have a common term of $\"4x-3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-3x%2B16x-12\"$ factors to $\"%28x%2B4%29%284x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"4x%5E2%2B13x-12\"$ factors to $\"%28x%2B4%29%284x-3%29\"$ (since $\"4x%5E2%2B13x-12\"$ is equivalent to $\"4x%5E2-3x%2B16x-12\"$ )
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