document.write( "Question 1183411: By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x. Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1 \n" ); document.write( "

Algebra.Com's Answer #813721 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "(a) By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x. \r
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\n" ); document.write( "\n" ); document.write( "(b) Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1
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document.write( "(a)  According to the remainder theorem, the remainder of  3(x+4)^2-(1-x)^3  when divided by x is the value \r\n" );
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document.write( "     of this polynomial at x= 0.\r\n" );
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document.write( "     So, we substitute the value of 0 instead of  x  into the polynomial and calculate\r\n" );
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document.write( "            =  = 3*16 - 1 = 48 - 1 = 47.      ANSWER\r\n" );
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document.write( "(b)  According to the remainder theorem, the remainder of  (2x-1)^3+6(3+4x)^2-10  when divided by  (2x+1)  is the value \r\n" );
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document.write( "     of this polynomial at x= -0.5,  which is the root of the binomial (2x+1).\r\n" );
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document.write( "     So, we substitute the value of  -0.5  instead of  x  into the polynomial and calculate\r\n" );
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document.write( "            =  = -8 + 6 - 10 = -12.      ANSWER\r\n" );
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