a, x^9 +x^3+x^2+1= x^9+x^8-x^8-x^7+x^7+x^6-x^6-x^5+x^5+x^4-x^4-x^3+2x^3+2x^2-x^2-x+x+1= x^8(x+1)-x^7(x+1)+x^6(x+1)-x^5(x+1)+x^4(x+1)-x^3(x+1)+2x^2(x+1)-x(x+1)+(x+1) = làm nốt
b, x^4-24x+48= dùng phương pháp hệ số bất định, hơi dài @@
c, x^7+x^2+1=(x^7 – x) + (x^2 + x + 1)
= x.(x^6 – 1) + (x^2 + x +1)
= x.(x^3 - 1).(x^3 +1) + (x^2 + x +1)
= x.(x-1).(x^2 + x +1).(x^3 +1) + (x^2 + x +1)
= (x^2 + x +1).[x.(x-1).(x^3 +1) + 1]
= (x^2 + x +1).[(x^2-x).(x^3 +1) + 1]
= (x^2 + x +1).(x^5-x^4 + x^2 -x + 1)
d, 2x^3-3x^2+1=2x^3-2x^2-x^2+1= 2x^2(x-1) -(x^2-1)= 2x^2(x-1) - (x+1)(x-1)= làm tiếp
e, x^2y^3+xy-x^2-x+y-1= (x^2y^3-x^2) +(y-1) +(xy-x) = x^2(y^3-1)+(y-1)+x(y-1) = x^2(y-1)(y^2+y+1)+(y-1)+x(y-1)= lm típ
f, x^3+y^3+6xy-8= x^3+y^3+3xy(x+y)+6xy-8-3xy(x+y)=[tex]\rightarrow (x+y-2)[(x+y)^2+2(x+y)+4]-3xy(x+y-2)[/tex] =[tex](x+y-2)(x^2+y^2-xy+2x+2y+4)=0[/tex]