\(x^{50}+x^{10}+1=x^{20}\left(x^{30}-1\right)+\left(x^{20}+x^{10}+1\right)\)
\(=x^{20}\left(x^{10}-1\right)\left(x^{20}+x^{10}+1\right)+\left(x^{20}+x^{10}+1\right)\)
\(=\left(x^{20}+x^{10}+1\right)\left(x^{30}-x^{20}+1\right)⋮\left(x^{20}+x^{10}+1\right)\forall x\)
Chứng minh rằng: \(x^{50}+x^{10}+1⋮x^{20}+x^{10}+1\)
Chứng minh:
a,\(x^{10}-10x+9⋮\left(x-1\right)^2\)
b,\(x^{50}+x^{10}+1⋮x^{20}+x^{10}+1\)
Chứng minh:
a) \(\left(x^{50}+x^{10}+1\right)⋮\left(x^{20}+x^{10}+1\right)\)
b) \(\left(x^{10}-10x+9\right)⋮\left(x^2+1\right)\)
c) \(\left(x+1\right)^{4n+2}+\left(x-1\right)^{4n+2}⋮\left(x^2+1\right)\)
14 Chứng minh rằng (x^2+x-1)^10+(x^2-x+1)^10 chia hết cho x-1
14 Chứng minh rằng \(\left(x^2+x-1\right)^{10}+\left(x^2-x+1\right)^{10}+1\) chia hết cho \(x^2-1\)
cm
\(x^{50}+x^{10}+x⋮x^{20}+x^{10}+1\)
Chứng minh rằng:
a, F(x)= x400 + x200 + 1 chia hết cho G(x)= x4 + x2 + 1
b, F(x)= x1970 + x1930 + x1890 chia hết cho G(x)= x20 + x10 + 1
Chứng minh rằng:
\(xA-A=x^{11}-1\) biết \(A=1+x+x^2+....+x^{10}\)
Chứng minh rằng: \(x^{10}-10x+9⋮\left(x-1\right)^2\)
