Đáp án:
Giải thích các bước giải:
`a) x^3+2x^2+x=x(x^2+2x+1)=x(x+1)^2`
`b) xy+y^2-x-y=y(x+y)-(x+y)=(x+y)(y-1)`
`c) x^5+x^4+1`
`= x ^5 + x ^4 + x ^2 − x ^2 + 1`
`= x^ 2 ( x^ 3 − 1 ) + ( x^ 4 + x ^2 + 1 )`
`=x^2( x-1)(x^2+x+1)+(x^4+2x^2+1-x^2)`
`= ( x^ 3 − 1 ) ( x ^2 + x + 1 ) + [ ( x ^2 + 1 )^ 2 − x ^2 ]`
`= ( x ^3 − 1 ) ( x ^2 + x + 1 ) + ( x ^2 + x + 1 ) ( x^ 2 − x + 1 )`
`= ( x ^2 + x + 1 ) ( x ^3 − 1 + x^ 2 − x + 1 )`
`= ( x ^2 + x + 1 ) ( x^ 3 + x ^2 − x )`
`= x ( x ^2 + x + 1 ) ( x^ 2 + x − 1 )`
