Bạn/anh/chị giúp em gấp bài này ạ
Em cảm ơn.
View attachment 160994
a) $x^{50}+x^{10}+1=x^50-x^{20}+(x^{20}+x^{10}+1) = (x^{30}-x^{20})(x^{20}+x^{10}+1)+(x^{20}+x^{10}+1) = (x^{20}+x^{10}+1)(x^{30}-x^{20}+1)$
b) $x^{2}-x^{9}-x^{1945} = -x^{1945}+x+x^{9}-1+(x^{2}-x+1) = -x[(x^{972})^{2}-1]-(x^{3}+1)(x^{6}+x^{3}+1)+(x^{2}-x+1)= -x(x^{972}+1)(x^{962}-1)-(x+1)(x^{2}-x+1)(x^{6}+x^{3}+1)+(x^{2}-x+1)$
Do $x^{972}+1 = (x^{3})^{324} +1$ chia hết cho $x^{3}+1$
Mà $x^{3}+1$ chia hết cho $x^{2}-x+1$
=> đpcm
c) x khác 1
$x^{10}-10x+9 = (x^{10}-x)-(9x-9) = x(x^{9}-1)-9(x-1) = x(x-1)(x^{8}+x^{7}+.....+x+1)-9(x-1) = (x-1)(x^{9}+x^{8}+......+x-9)$
Ta có: $(x^{9}+x^{8}+......+x-9) = (x^{9}-1)+(x^{8}-1)+......+(x-1)$ chia hết cho x-1 (Do $x^{n}-1$ chia hết cho x-1)
=> $(x-1)(x^{9}+x^{8}+......+x-9)$ chia hết cho $(x-1)^{2}$ (đpcm)
d)$....=8x^{8}(x-1)-(x^{8}-1) = 8x^{8}(x-1) - (x-1)(x^{7}+....+x+1) = (x-1)(8x^{8}-x^{7}-x^{6}-....-x-1) = (x-1)[(x^{8}-x^{7})+(x^{8}-x^{6})+.....+(x^{8}-x)+(x^{8}-1)] = (x-1)[x^{7}(x-1)+x^{6}(x^{2}-1)+......+x(x^{7}-1)+x^{8}-1] = (x-1)(x^{7}(x-1)+x^{6}.(x-1)(x+1)+.....+x(x-1)(x^{6}+x^{5}+....+1)+(x-1)(x^{7}+x^{6}+...+1)] = (x-1)[(x-1)(8x^{7}+7x^{6}+....+2x+1)]$ chia hết cho $(x-1)^{2}$ (đpcm)
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
