Phân tích đa thức thành nhân tử a)x ² – y ² -5x+5y b)a(x ² +1)-x (a ² +1) c)x^4 +2010x ² +2009x+2010 15/07/2021 Bởi Gianna Phân tích đa thức thành nhân tử a)x ² – y ² -5x+5y b)a(x ² +1)-x (a ² +1) c)x^4 +2010x ² +2009x+2010
Đáp án+Giải thích các bước giải: `a)` `x^2-y^2-5x+5y` `=(x-y)(x+y)-5(x-y)` `=(x-y)(x+y-5)` `b)` `a(x^2+1)-x(a^2+1)` `=ax^2+a-a^2x-x` `=(ax^2-a^2x)+(a-x)` `=-ax(a-x)+(a-x)` `=(a-x)(1-ax)` `c)x^4+2010x^2+2009x+2010` `=x^4-x+2010x^2+2010x+2010` `=x(x^3-1)+2010(x^2+x+1)` `=x(x-1)(x^2+x+1)+2010(x^2+x+1)` `=(x^2+x+1)[x(x-1)+2010]` `=(x^2+x+1)(x^2-x+2010)` Bình luận
a)x²-y²-5x+5y =(x+y)(x-y)-5(x-y) =(x+y-5)(x-y) b)a(x²+1)-x(a²+1) =ax²+a-xa²-x =ax(x-a)-(x-a) =(x-a)(ax-1) c)$x^{4}$ +2010x²+2009x+2010 =$x^{4}$+2010x²+2010x-x+2010 =($x^{4}$-x)+(2010x²+2010x+2010) =x(x³-1)+2010(x²+x+1) =x(x-1)(x²+x+1)+2010(x²+x+1) =(x²+x+1)(x(x-1)+2010) =(x²+x+1)(x²-x+2010) Bình luận
Đáp án+Giải thích các bước giải:
`a)`
`x^2-y^2-5x+5y`
`=(x-y)(x+y)-5(x-y)`
`=(x-y)(x+y-5)`
`b)`
`a(x^2+1)-x(a^2+1)`
`=ax^2+a-a^2x-x`
`=(ax^2-a^2x)+(a-x)`
`=-ax(a-x)+(a-x)`
`=(a-x)(1-ax)`
`c)x^4+2010x^2+2009x+2010`
`=x^4-x+2010x^2+2010x+2010`
`=x(x^3-1)+2010(x^2+x+1)`
`=x(x-1)(x^2+x+1)+2010(x^2+x+1)`
`=(x^2+x+1)[x(x-1)+2010]`
`=(x^2+x+1)(x^2-x+2010)`
a)x²-y²-5x+5y
=(x+y)(x-y)-5(x-y)
=(x+y-5)(x-y)
b)a(x²+1)-x(a²+1)
=ax²+a-xa²-x
=ax(x-a)-(x-a)
=(x-a)(ax-1)
c)$x^{4}$ +2010x²+2009x+2010
=$x^{4}$+2010x²+2010x-x+2010
=($x^{4}$-x)+(2010x²+2010x+2010)
=x(x³-1)+2010(x²+x+1)
=x(x-1)(x²+x+1)+2010(x²+x+1)
=(x²+x+1)(x(x-1)+2010)
=(x²+x+1)(x²-x+2010)