Algebra.Com's Answer #268169 by jsmallt9(3758)![\"\"](\"/images/stars/stars-13.gif\")   You can put this solution on YOUR website! The straightforward way to find a remainder is to divide. But because of the range of exponents in the polynomial this is not the simple way to find the remainder. After all, look at what the synthetic division would look like: \n" ); document.write( " \r\n" ); document.write( "-1 | 9 0 0 0 0 0 0 0 0 0 0 -7 0 0 0 0 0 0 -2 0 0 0 0 1\r\n" ); document.write( "----\r\n" ); document.write( " -------------------------------------------------\r\n" ); document.write( " \n" ); document.write( "This will work but it is tedious. \n" ); document.write( "The fast way to find the remainder is to take advantage of the Remainder Theorem and advantage of how easy it is to raise -1 to high powers. The Remainder Theorem tells us that if one divides a polynomial by (x-r) then the remainder is the value of that polynomial for x = r. So the remainder when \n" ); document.write( " \n" ); document.write( "(Note if x was not 1 or -1, this method is not easy because raising other numbers to the 23rd, 12th and 5th powers are not simple.) \n" ); document.write( "Simplifying... \n" ); document.write( "9(-1) - 7(+1) - 2(-1) + 1 \n" ); document.write( "-9 - 7 + 2 + 1 \n" ); document.write( "-13 \n" ); document.write( "The value of the polynomial, when x = -1, is -13. So the remainder when dividing the polynomial by (x+1) will also be -13. \n" ); document.write( " |