document.write( "Question 458319: I have the answer to this. Division of polynomial but I think I am messing up the steps. (#1)1-3x^2/x+2 answer -3x+6-11/x+2. (#2) the product of twice a number and three is the same as the diffrence of five times the number and 3/4. Find the number. (#3). Solution or equation, I have the answer need help setting it up. x-3/7=-2: -11 thank you very much. A greatful mom. \n" ); document.write( "
Algebra.Com's Answer #314426 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
I have the answer to this. Division of polynomial but I think I am messing up the steps. (#1)1-3x^2/x+2 answer -3x+6-11/x+2. (#2) the product of twice a number and three is the same as the diffrence of five times the number and 3/4. Find the number. (#3). Solution or equation, I have the answer need help setting it up. x-3/7=-2: -11 thank you very much. A greatful mom.
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\n" ); document.write( "I have the answer to this. Division of polynomial but I think I am messing up the steps.
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document.write( "(#1)  1 - 3x²\r\n" );
document.write( "      ———————\r\n" );
document.write( "       x + 2\r\n" );
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document.write( "You must do two things with the numerator.\r\n" );
document.write( "1. Arrange it in descending powers of x.\r\n" );
document.write( "   Change it from 1 - 3x² to -3x² + 1 \r\n" );
document.write( "2. Insert a placeholder term of 0x to hold\r\n" );
document.write( "   the place for that term so you'll have\r\n" );
document.write( "the highest power term first, then the first\r\n" );
document.write( "power of x-term and then a constant number\r\n" );
document.write( "on the end like this -3x² + 0x + 1  \r\n" );
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document.write( "So we put this in an array with x + 2 as the\r\n" );
document.write( "divisor, and -3x² + 0x + 1 as the dividend.\r\n" );
document.write( "You say \"x+2 divided into -3x²+0x+1\"\r\n" );
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document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "    \r\n" );
document.write( "The x on the far left goes into -3x² and \r\n" );
document.write( "gives -3x because \"%28-3x%5E2%29%2Fx=-3x\". So\r\n" );
document.write( "we write -3x above the 0x, like this\r\n" );
document.write( "             \r\n" );
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document.write( "            -3x     \r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      \r\n" );
document.write( "Now multiply the -3x by both of the terms of x + 2.\r\n" );
document.write( "-3x(x + 2) = -3x² - 6x, so we write -3x² - 6x underneath\r\n" );
document.write( "the first two terms of the dividend, like this\r\n" );
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document.write( "            -3x     \r\n" );
document.write( "x + 2)-3x² + 0x +  1   \r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "            \r\n" );
document.write( "Now you draw a line underneath:\r\n" );
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document.write( "            -3x     \r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
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document.write( "Now you subtract those:\r\n" );
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document.write( "    (-3x² - 0x) - (-3x² - 6x) = -3x² - 0x + 3x² + 6x = 6x.\r\n" );
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document.write( "So you put 6x under the - 6x:\r\n" );
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document.write( "            -3x     \r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x \r\n" );
document.write( "             \r\n" );
document.write( "Now we do something like the first step. The x on\r\n" );
document.write( "the far left goes into 6x and gives 6 because \"%286x%29%2Fx=6\". So\r\n" );
document.write( "we write + 6 above the + 1, like this\r\n" );
document.write( "                 \r\n" );
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document.write( "            -3x +  6\r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x \r\n" );
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document.write( "Next we bring down the + 1 to the bottom, like this\r\n" );
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document.write( "            -3x +  6\r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x +  1\r\n" );
document.write( "             \r\n" );
document.write( "Now like in the 2nd step, we now multiply the 6 by both of \r\n" );
document.write( "the terms of x + 2.  6(x + 2) = 6x + 12, so we write 6x + 12 \r\n" );
document.write( "underneath the two terms at the bottom, like this\r\n" );
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document.write( "            -3x +  6\r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x +  1\r\n" );
document.write( "             6x + 12 \r\n" );
document.write( "         \r\n" );
document.write( "Next we draw a line underneath:\r\n" );
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document.write( "            -3x +  6\r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x +  1\r\n" );
document.write( "             6x + 12\r\n" );
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document.write( "        \r\n" );
document.write( "Now like in the 3rd step, we subtract those: \r\n" );
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document.write( "(6x + 1) - (6x + 12) = 6x + 1 - 6x - 12 = -11 So you put -11 under the + 12:\r\n" );
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document.write( "            -3x +  6\r\n" );
document.write( "x + 2)-3x² + 0x +  1\r\n" );
document.write( "      -3x² - 6x\r\n" );
document.write( "             6x +  1\r\n" );
document.write( "             6x + 12 \r\n" );
document.write( "                 -11\r\n" );
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document.write( "-11 is the remainder. And you're done with the division \r\n" );
document.write( "algorithm but that's not all you do.  You have to interpret \r\n" );
document.write( "a division of this form:\r\n" );
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document.write( "        QUOTIENT   \r\n" );
document.write( "DIVISOR)DIVIDEND\r\n" );
document.write( "        ...\r\n" );
document.write( "            ....\r\n" );
document.write( "        REMAINDER\r\n" );
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document.write( "as \r\n" );
document.write( "           REMAINDER \r\n" );
document.write( "QUOTIENT + —————————  \r\n" );
document.write( "            DIVISOR           \r\n" );
document.write( "           \r\n" );
document.write( "or\r\n" );
document.write( "           -11\r\n" );
document.write( "-3x + 6 + ————— \r\n" );
document.write( "          x + 2 \r\n" );
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document.write( "And since the numerator of the fraction is negative,\r\n" );
document.write( "you can just change the plus sign before the fraction\r\n" );
document.write( "to a minus, and get:\r\n" );
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document.write( "            11\r\n" );
document.write( "-3x + 6 - ————— \r\n" );
document.write( "          x + 2\r\n" );
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document.write( "(#2) the product of twice a number and three is the same as the diffrence of five times the number and ¾. \r\n" );
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document.write( "Replace the words \"a number\" and \"the number\" with a letter variable,\r\n" );
document.write( "say N, and rewrite it:\r\n" );
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document.write( "(#2) the product of twice N and three is the same as the difference of five times N and ¾.\r\n" );
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document.write( "Now we replace the words \"twice N\" with \"2N\" and the words \"five times N\"\r\n" );
document.write( "by \"5N\", and the word \"three\" by \"3\" and rewrite it:\r\n" );
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document.write( "(#2) the product of 2N and 3 is the same as the difference of 5N and ¾.\r\n" );
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document.write( "\"Product\" means to multiply and \"difference\" means to subtract. Therefore\r\n" );
document.write( "we replace the words \"The product of 2N and 3\" with \"(2N)·(3)\" and we\r\n" );
document.write( "replace the words \"the difference of 5N and ¾\" by \"5N-¾\"\r\n" );
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document.write( "     (2N)·(3) is the same as 5N-¾\r\n" );
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document.write( "Finally we replace the words \"is the same as\" by an equal sign \"=\":\r\n" );
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document.write( "     (2N)·(3) = 5N-¾\r\n" );
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document.write( "That's the equation.  So to solve it we replace (2N)·(3) by 6N:\r\n" );
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document.write( "     6N = 5N-¾\r\n" );
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document.write( "We clear of fractions by multiplying every term by the LCD of 4\r\n" );
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document.write( "    24N = 20N - 3\r\n" );
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document.write( "Subtract 20N from both sides:\r\n" );
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document.write( "     4N = -3\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "      N = -¾  \r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "         x - 3 \r\n" );
document.write( "(#3).    ————— = -2\r\n" );
document.write( "           7\r\n" );
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document.write( "Clear of fractions by multiplying every term on\r\n" );
document.write( "both sides by LCD = 7:\r\n" );
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document.write( "         x - 3 = -14\r\n" );
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document.write( "Add 3 to both sides:\r\n" );
document.write( "         \r\n" );
document.write( "             x = -11 \r\n" );
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document.write( "Edwin
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