Đợi nghĩ ra cách ngắn hơn nhá :))
\(1)\)\(B=x^{15}-8x^{14}+8x^{13}-8x^{12}+...-8x^2+8x-5\)
\(B=-7x^{15}+\left(8x^{15}-8x^{14}\right)+\left(8x^{13}-8x^{12}\right)+...+\left(8x^3-8x^2\right)+\left(8x-8\right)+3\)
\(B=-7x^{15}+8x^{14}\left(x-1\right)+8x^{12}\left(x-1\right)+...+8x^2\left(x-1\right)+8\left(x-1\right)+3\)
\(B=-7x^{15}+8\left(x-1\right)\left(x^{14}+x^{12}+...+x^2+1\right)+3\)
\(B=-7x^{15}+8\left(x-1\right)\left[x^{12}\left(x^2+1\right)+x^8\left(x^2+1\right)+...+\left(x^2+1\right)\right]+3\)
\(B=-7x^{15}+8\left(x-1\right)\left(x^2+1\right)\left(x^{12}+x^8+...+1\right)+3\)
\(B=-7x^{15}+8\left(x-1\right)\left(x^2+1\right)\left[x^8\left(x^4+1\right)+\left(x^4+1\right)\right]+3\)
\(x=7\)\(\Rightarrow\)\(x+1=8\)
\(B=-7x^{15}+\left(x+1\right)\left(x-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)+3\)
\(B=-7x^{15}+\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(B=-7x^{15}+\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(B=-7x^{15}+\left(x^8-1\right)\left(x^8+1\right)=-7x^{15}+x^{16}-1=x^{15}\left(x-7\right)-1=-1\)
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