document.write( "Question 1144428: Find the values of h and k given that x + 2 is a factor of Q(x) = (x + h)^2 + k, and the remainder is 16 when Q (x) is divided by x. \n" ); document.write( "

Algebra.Com's Answer #765599 by ikleyn(52909) $\"\"$ $\"About$

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document.write( "Q(x) =  = .\r\n" );
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document.write( "The fact that this polynomial gives the remainder 16, when it is divided by x,  means that\r\n" );
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document.write( "    h^2 + k = 16.         (1)\r\n" );
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document.write( "Then the polynomial takes the form\r\n" );
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document.write( "    Q(x) = .    (2)\r\n" );
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document.write( "Next, we are given that (x+2) divides this polynomial.\r\n" );
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document.write( "It means that x= -2 is its root  (the Remainder Theorem).\r\n" );
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document.write( "Write this equation Q(-2) = 0.  Due to  (2),  it takes the form\r\n" );
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document.write( "    ((-2)^2 + 2h*(-2) + 16 = 0.\r\n" );
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document.write( "Simplify and find \"h\" :\r\n" );
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document.write( "     4     - 4h + 16 = 0,\r\n" );
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document.write( "             4h = 16 + 4\r\n" );
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document.write( "             4h = 20\r\n" );
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document.write( "              h =  = 5.\r\n" );
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document.write( "Now substitute this value  h= 5  into formula (1). You will get\r\n" );
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document.write( "    5^2 + k = 16,\r\n" );
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document.write( "    25 + k = 16,\r\n" );
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document.write( "         k = 16 - 25 = -9.\r\n" );
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document.write( "ANSWER.  h= 5;  k= = -9.\r\n" );
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