document.write( "Question 450013: find the value of p and q when the polynomial (x*x*x)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2. \n" ); document.write( "
Algebra.Com's Answer #309587 by stanbon(75887)\"\" \"About 
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find the value of p and q when the polynomial (x*x*x)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2.
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\n" ); document.write( "Polynomial x^3 + px^2 + qx + 6
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\n" ); document.write( "Using synthetic division:
\n" ); document.write( "3)....1....p......q.......6
\n" ); document.write( ".......1....p+3..3(p+3)+q..|9(p+3)+3q +6
\n" ); document.write( "----
\n" ); document.write( "Equation:
\n" ); document.write( "9p + 3q + 33 = 3
\n" ); document.write( "3p + q = -10
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\n" ); document.write( "2)....1....p.......q........6
\n" ); document.write( ".......1...p+2..2(p+2)+q...|4(p+2)+2q+6
\n" ); document.write( "------
\n" ); document.write( "Equation:
\n" ); document.write( "4p+2q = -14
\n" ); document.write( "2p+q = -7
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\n" ); document.write( "Solve the system:
\n" ); document.write( "3p+q = -10
\n" ); document.write( "2p+q = -7
\n" ); document.write( "Subtract to get:
\n" ); document.write( "p = -3
\n" ); document.write( "---
\n" ); document.write( "Solve for \"q\":
\n" ); document.write( "2p+q = -7
\n" ); document.write( "2*-3 + q = -7
\n" ); document.write( "-6 + q = -7
\n" ); document.write( "q = -1
\n" ); document.write( "====================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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