Toán Lớp 8: tách các hạng tử a^4+a^2+2a x^2+4x-5 6x^2-5x+1 4x^4+1 x^5+x+1 giúp mình đi please

Question

Toán Lớp 8:  tách các hạng tử a^4+a^2+2a x^2+4x-5 6x^2-5x+1 4x^4+1 x^5+x+1 giúp mình đi please

lanminhngoc · Answer

***Lời giải***   a)    a^4+a^2+2a     =a.a^3+a.a+2a     =a(a^3+a+2)     b)     x^2+4x-5     =(x^2+x)+(-5x-5)     =x(x+1)-5(x+1)     =(x-5)(x+1)     c)     6x^2-5x+1     =(6x^2-3x)+(-2x+1)     =3x(2x-1)-(2x-1)     =(3x-1)(2x-1)     d)     4x^4+1     =4x^4+4x^3-4x^3+4x^2-4x^2-2x+2x+1     =(4x^4+4x^3+2x^2)+(-4x^3-4x^2-2x)+(2x^2+2x+1)     =2x^2(2x^2+2x+1)-2x(2x^2+2x+1)+2x^2+2x+1     =(2x^2-2x+1)(2x^2+2x+1)     e)     x^5+x+1     =(x^5-x^2)+x^2+x+1     =x^2(x^3-1)+(x^2+x+1)     =x^2(x-1)(x^2+x+1)+(x^2+x+1)    =(x^2+x+1)[x^2(x-1)+1]    =(x^2+x+1)(x^3-x^2+1)

maingocquynhnhu2k1 · Answer

#Sad   a)   a^4+a^2+2a   = a(a^3+a+2)   b)   x^2+4x-5   = x^2+5x-x-5   = (x^2+5x)-(x+5)   = x(x+5)-(x+5)   = (x-1)(x+5)   c)   6x^2-5x+1   = 6x^2-3x-2x+1   = (6x^2-3x)-(2x-1)   = 3x(2x-1)-(2x-1)   = (3x-1)(2x-1)   d)   4x^4+1   = (4x^4+4x^2+1)-4x^2   = [(2x^2)^2+2. 2x^2. x+1^2]-(2x)^2   = (2x^2+1)^2-(2x)^2   = (2x^2-2x+1)(2x^2+2x+1)   e)   x^5+x+1   = x^5-x^2+x^2+x+1   = (x^5-x^2)+(x^2+x+1)   = x^2(x^3-1)+(x^2+x+1)   = x^2(x-1)(x^2+x+1)+(x^2+x+1)   = (x^2+x+1)(x^3-x^2+1)