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
\n" ); document.write( "\n" ); document.write( "Using synthetic division, I identified that for x+2; \r
\n" ); document.write( "\n" ); document.write( "Equation 1: 4p+16-2q-40\r
\n" ); document.write( "\n" ); document.write( "Equation 2: -25p+5q+585\r
\n" ); document.write( "\n" ); 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
\n" ); document.write( "\n" ); document.write( "For example, 4p-25p=-21p and 5q-2q=3q\r
\n" ); document.write( "\n" ); document.write( "However, in the case of 3p+27-q and -p-1+q\r
\n" ); document.write( "\n" ); 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)\"\" \"About 
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.
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