Đáp án :
`a)A=(x-2)^2(x^2+2x+2)`
`b)B=(x^2+x+1)(x^6-x^5+x^3-x+1)`
`c)C=x^3[6(x+1/x)^2+5(x+1/x)+1/x^3+8]`
Giải thích các bước giải :
`a)A=(x^2-x-2)^2+(x-2)^2`
`<=>A=[(x-2)(x+1)]^2+(x-2)^2`
`<=>A=(x-2)^2×(x+1)^2+(x-2)^2`
`<=>A=(x-2)^2[(x+1)^2+1]`
`<=>A=(x-2)^2(x^2+2x+2)`
`b)B=x^8+x^4+1`
`<=>B=(x^8-x^2)+(x^4-x)+(x^2+x+1)`
`<=>B=x^2(x^6-1)+x(x^3-1)+(x^2+x+1)`
`<=>B=x^2[(x^3)^2-1^2]+x(x^3-1)+(x^2+x+1)`
`<=>B=x^2(x^3-1)(x^3+1)+x(x^3-1)+(x^2+x+1)`
`<=>B=x^2(x^3+1)(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+(x^2+x+1)`
`<=>B=(x^2+x+1)[x^2(x^3+1)(x-1)+x(x-1)+1]`
`<=>B=(x^2+x+1)(x^6-x^5+x^3-x^2+x^2-x+1)`
`<=>B=(x^2+x+1)(x^6-x^5+x^3-x+1)`
`c)C=6x^5+5x^4+20x^3+5x^2+6x+1`
`<=>C/x^3=(6x^5+5x^4+20x^3+5x^2+6x+1)/x^3`
`<=>C/x^3=6x^2+5x+20+5/x+6/(x^2)+1/x^3`
`<=>C/x^3=(6x^2+6/(x^2))+(5x+5/x)+1/x^3+20`
`<=>C/x^3=6(x^2+1/(x^2))+5(x+1/x)+1/x^3+20`
`<=>C/x^3=6(x^2+2+1/(x^2)-2)+5(x+1/x)+1/x^3+20`
`<=>C/x^3=6(x+1/x)^2-12+5(x+1/x)+1/x^3+20`
`<=>C/x^3=6(x+1/x)^2+5(x+1/x)+1/x^3+8`
`<=>C=x^3[6(x+1/x)^2+5(x+1/x)+1/x^3+8]`
~Chúc bạn học tốt !!!~
