document.write( "Question 935110: I have been asked to show that (x+2) and (x-5) are factors of x^4+px^2+qx-40\r
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document.write( "Using synthetic division, I identified that for x+2; \r
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document.write( "Equation 1: 4p+16-2q-40\r
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document.write( "Equation 2: -25p+5q+585\r
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document.write( "However, if I were to subtract Equation 1 from 2; I do not have either P or Q fully nullified, there is a remainder left over.\r
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document.write( "For example, 4p-25p=-21p and 5q-2q=3q\r
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document.write( "However, in the case of 3p+27-q and -p-1+q\r
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document.write( "The -q and +q cancel each other out; leaving us only with the unknown P variable term. How would I remedy/rectify such a situation?\r
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Algebra.Com's Answer #568234 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! show that (x+2) and (x-5) are factors of x^4+px^2+qx-40 \n" ); document.write( "---- \n" ); document.write( "Using synthetic division:: \n" ); document.write( "-2)....1....0....p....q....-40 \n" ); document.write( ".......1....8...p-16..q-2p+32..-40-2q+4p-64 \n" ); document.write( "------ \n" ); document.write( "Equation: \n" ); document.write( "4p - 2q + 24 = 0 \n" ); document.write( "----------------------------- \n" ); document.write( "5)....1....0....p.........q........-40 \n" ); document.write( "......1....5....p+25.....q+5p+125..-40+5q + 25p + 625 \n" ); document.write( "---- \n" ); document.write( "Equation:: \n" ); document.write( "25p + 5q +585 = 0 \n" ); document.write( "------ \n" ); document.write( "System of equations in p and q:: \n" ); document.write( "2p - q = -12 \n" ); document.write( "5p + q = -117 \n" ); document.write( "----- \n" ); document.write( "Add and solve for \"p\":: \n" ); document.write( "7p =-129 \n" ); document.write( "p = -129/7 \n" ); document.write( "----- \n" ); document.write( "Solve for \"q\": \n" ); document.write( "2p - q = -12 \n" ); document.write( "-258/7 - q = -12 \n" ); document.write( "-258/7 - q = -84/7 \n" ); document.write( "q = -174/7 \n" ); document.write( "------------------ \n" ); document.write( "Cheers, \n" ); document.write( "Stan H. \n" ); document.write( "---------------\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |