Ta có : \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-2015\)
\(=\left(x^2+2x+3x+6\right)\left(x^2+4x+5x+20\right)-2015\)
\(=\left(x^2+5x+6\right)\left(x^2+9x+20\right)-2015\)
\(=x^4+5x^3+6x^2+9x^3+45x^2+54x+20x^2+100x+120-2015\)
\(=x^4+14x^3+71x^2+154x-1895\)
\(=\left(x^4+7x^3-2x^2\right)+\left(73x^2+511x-146\right)+\left(7x^3+49x^2-14x\right)-\left(49x^2+343x-98\right)-1847\)
\(=x^2\left(x^2+7x-2\right)+73\left(x^2+7x-2\right)+7x\left(x^2+7x-2\right)-49\left(x^2+7x-2\right)-1847\)
\(=\left(x^2+73+7x-49\right)\left(x^2+7x-2\right)-1847\)
Vậy số dư khi chia là 1847
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