document.write( "Question 1144164: Predict the quotient of x^5+2x^4+2x^3+2x^2+2x+1÷x+1. Explain your prediction. \n" ); document.write( "
Algebra.Com's Answer #765169 by greenestamps(13334)\"\" \"About 
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\n" ); document.write( "Prediction:

\n" ); document.write( "Explanation....

\n" ); document.write( "Look at the familiar product when (x+1) is multiplied by (x+1) and like terms are combined in the product:
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document.write( "(x+1)(x+1) = x^2 + x\r\n" );
document.write( "           +       x + 1\r\n" );
document.write( "           --------------\r\n" );
document.write( "             x^2 +2x + 1

\n" ); document.write( "Now look what we get when (x^2+x+1) is multiplied by (x+1):
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document.write( "(x^2+x+1)(x+1) = x^3 + x^2 + x \r\n" );
document.write( "               +       x^2 + x + 1\r\n" );
document.write( "                -------------------\r\n" );
document.write( "                 x^3 +2x^2 +2x + 1

\n" ); document.write( "You should be able to see that, as more powers of x are added to the first factor, the pattern of the product will continue. So in particular
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document.write( "x^4+x^3+x^2+x+1)(x+1) = x^5 + x^4 + x^3 + x^2 + x\r\n" );
document.write( "                      +       x^4 + x^3 + x^2 + x + 1\r\n" );
document.write( "                      -------------------------------\r\n" );
document.write( "                        x^5 +2x^4 +2x^3 +2x^2 +2x + 1

\n" ); document.write( "And so

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