document.write( "Question 628062: Use synthetic division and the remainder theorem to find the value of the given function\r
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\n" ); document.write( "formula is : f(x)=x^4+3x^2+5 \n" ); document.write( "
Algebra.Com's Answer #395352 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "f(x) = x4 + 3x2 + 5\r\n" );
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document.write( "Synthetic division\r\n" );
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document.write( "To do synthetic division with this polynomial you must insert\r\n" );
document.write( "zero placeholders for the missing 3rd and 1st powers of x.\r\n" );
document.write( "of x:\r\n" );
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document.write( "f(x) = x4 + 0x3 + 3x2 + 0x + 5\r\n" );
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document.write( "-3|1  0  3   0   5\r\n" );
document.write( "  |  -3  9 -36 108\r\n" );
document.write( "   1 -3 12 -36 113\r\n" );
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document.write( "Answer: f(-3) = 113\r\n" );
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document.write( "Check by direct substitution:\r\n" );
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document.write( "f(x) = x4 + 3x2 + 5\r\n" );
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document.write( "f(-3) = (-3)4 + 3(-3)2 + 5\r\n" );
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document.write( "f(-3) = 81 + 3·9 + 5 = 81 + 27 + 5 = 113\r\n" );
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document.write( "So it checks.  The remainder when using a number with synthetic division\r\n" );
document.write( "will always give the same answer as substituting that number for x directly.\r\n" );
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document.write( "Edwin
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