Toán Lớp 8: phân tích đa thức thành nhân tử a, x7+x2+1 b, x10+x5+1 c, x7+x5+1 d, x5+x+1

Question

Toán Lớp 8:  phân tích đa thức thành nhân tử a, x7+x2+1 b,  x10+x5+1  c, x7+x5+1 d, x5+x+1

minhtuyethue · Answer

Giải đáp:a, x7+x2+1=(x7 &ndash; x) + (x2 + x + 1)   = x.(x6 &ndash; 1) + (x2 + x +1)   = x.(x3 - 1).(x3 +1) + (x2 + x +1)   = x.(x-1).(x2 + x +1).(x3 +1) + (x2 + x +1)   = (x2 + x +1).[x.(x-1).(x3 +1) + 1]   = (x2 + x +1).[(x2-x).(x3 +1) + 1]   = (x2 + x +1).(x5-x4 + x2 -x + 1)     b,x10+x5+1    =x10+x5+1+x2-x-x   =(x10-x)+(x5-2)+(x2+x+1)    =x(x9)-1+x2 (x3-1)+(x2+x+1)   =x(x6+x3+1)(x3-1)+x2(x-1)(x2+x+1)+(x2+x+1)   =(x7+x4+x) (x2+x+1) (x-1)+(x3-x2)(x2+x+1)+(x2+x+1)   =(x2+x+1)(x8-x7-x5-x4-x2-x-x3-x2+1)   =(x2+x+1)(x8-x7-x5-x4-x-x3+1)   Lời giải và giải thích chi tiết:

quynhmaithu · Answer

a)   x 7 +x 2 +1     = x 7 +x 6 +x 5 -x 6 -x 5 -x 4 +x 4 +x 3 +x 2 -x 3 -x 2 -x+x 2 +x+1     = x 5 (x 2 +x+1)-x 4 (x 2 +x+1)+x 2 (x 2 +x+1)-x(x 2 +x+1)+(x 2 +x+1)     = (x 2 +x+1)(x 5 -x 4 +x 2 -x+1)     b)   x 10 +x 5 +1     = x 10 +x 9 +x 8 -x 9 -x 8 -x 7 +x 7 +x 6 +x 5 -x 6 -x 5 -x 4 +x 5 +x 4 +x 3 -x 3 -x 2 -x+x 2 +x+1     = x 8 (x 2 +x+1) - x 7 (x 2 +x+1)+x 5 (x 2 +x+1)-x 4 (x 2 +x+1)+x 3 (x 2 +x +1)-x(x 2 +x+1)+(x 2 +x+1)       = (x 2 +x+1)(x 8 -x 7 +x 5 -x 4 +x 3 +x+1)       c)     x 7 +x 5 +1       = x 7 +x 6 +x 5 -x 6 -x 5 -x 4 +x 5 +x 4 +x 3 -x 3 -x 2 -x+x 2 +x+1       = x 5 (x 2 +x+1)-x 4 (x 2 +x+1)+x 3 (x 2 +x+1)-x(x 2 +x+1)+(x 2 +x+1)       = (x 2 +x+1)(x 5 -x 4 +x 3 -x+1)       d)     x 5 +x+1       = x 5 +x 4 +x 3 -x 4 -x 3 -x 2 +x 2 +x+1       = x 3 (x 2 +x+1)-x 2 (x 2 +x+1)+(x 2 +x+1)       = (x 2 +x+1)(x 3 -x 2 +1)       &hearts; Ch&uacute;c bạn học tốt. Cho mk xin TLHN &hearts;