Question

if the polynomial x^19+x^17+x^13+x^11+x^7+x^5x^3is divided by x^2+1 find the remainder​

Answer 1

Answer:

${x}^{19} + {x}^{17} + {x}^{13} + {x}^{11} + {x}^{7} + {x}^{5} + {x}^{3} = \\ {x}^{17} ( {x}^{2} + 1) + {x}^{11} ( {x}^{2} + 1) + {x}^{5} ( {x}^{2} + 1) + {x}^{3} = \\ ( {x}^{2} + 1)( {x}^{17} + {x}^{11} + {x}^{5} ) + {x}^{3} \\ so \: \: required \: remainder = {x}^{3}$