document.write( "Question 133352: 64x^3+343\r
\n" ); document.write( "\n" ); document.write( "x^4+8x^2-9\r
\n" ); document.write( "\n" ); document.write( "these are the two polynomials im left with!
\n" ); document.write( "pleasee help!
\n" ); document.write( "thankss! \n" ); document.write( "

Algebra.Com's Answer #97539 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( " $\"64x%5E3%2B343\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%29%5E3%2B%287%29%5E3\"$ Rewrite $\"64x%5E3\"$ as $\"%284x%29%5E3\"$ . Rewrite $\"343\"$ as $\"%287%29%5E3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%2B7%29%28%284x%29%5E2-%284x%29%287%29%2B%287%29%5E2%29\"$ Now factor by using the sum of cubes formula. Remember the sum of cubes formula is $\"A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%2B7%29%2816x%5E2-28x%2B49%29\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( "So $\"64x%5E3%2B343\"$ factors to $\"%284x%2B7%29%2816x%5E2-28x%2B49%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"64x%5E3%2B343=%284x%2B7%29%2816x%5E2-28x%2B49%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E4%2B8x%5E2-9\"$ we can see that the first term is $\"1x%5E4\"$ and the last term is $\"-9\"$ where the coefficients are 1 and -9 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -9 to get -9. Now what two numbers multiply to -9 and add to the middle coefficient 8? Let's list all of the factors of -9:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -9:\r
\n" ); document.write( "\n" ); document.write( "1,3\r
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\n" ); document.write( "\n" ); document.write( "-1,-3 ...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 -9\r
\n" ); document.write( "\n" ); document.write( "(1)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(9)\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 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	-9	1+(-9)=-8
-1	9	-1+9=8

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -1 and 9 add up to 8 and multiply to -9\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E4%2B8x%5E2-9\"$ , replace $\"8x%5E2\"$ with $\"-1x%5E2%2B9x%5E2\"$ (notice $\"-1x%5E2%2B9x%5E2\"$ adds up to $\"8x%5E2\"$ . So it is equivalent to $\"8x%5E2\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E4%2Bhighlight%28-1x%5E2%2B9x%5E2%29%2B-9\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E4-1x%5E2%2B9x%5E2-9\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E4-1x%5E2%29%2B%289x%5E2-9%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28x%5E2-1%29%2B9%28x%5E2-1%29\"$ Factor out the GCF of $\"x%5E2\"$ out of the first group. Factor out the GCF of $\"9\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B9%29%28x%5E2-1%29\"$ Since we have a common term of $\"x%5E2-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E4-1x%5E2%2B9x%5E2-9\"$ factors to $\"%28x%5E2%2B9%29%28x%5E2-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E4%2B8x%5E2-9\"$ factors to $\"%28x%5E2%2B9%29%28x%5E2-1%29\"$ (since $\"1x%5E4%2B8x%5E2-9\"$ is equivalent to $\"1x%5E4-1x%5E2%2B9x%5E2-9\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E4%2B8x%5E2-9\"$ factors to $\"%28x%5E2%2B9%29%28x%5E2-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B9%29%28x%2B1%29%28x-1%29\"$ Now factor $\"x%5E2-1\"$ by using the difference of squares\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E4%2B8x%5E2-9\"$ factors to $\"%28x%5E2%2B9%29%28x%2B1%29%28x-1%29\"$ \n" ); document.write( "

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