phan tich da thuc thanh nhan tu x^4+4 x^5+x+1 a^4+64 x^5+x-1

hiennhanoncetwice

2 năm trước

Loga Sinh Học lớp 12

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buithien1203

Giải thích các bước giải:

$x^{4}$ +4

=$x^{4}$+4+4 $x^{2}$- 4$x^{2}$

=$(x^{2} +2)^{2}$ -4$x^{2}$

=($x^{2}$ +2-2x)($x^{2}$ +2+2x)

$x^{5}$ +x+1

=$x^{5}$ +$x^{2}$- $x^{2}$ +1

=$x^{2}$ ($x^{3}$ -1)+$x^{2}$ +x+1

= $x^{2}$ (x-1)($x^{2}$+1+1) + $x^{2}$ +x+1

= ($x^{2}$ +x+1)($x^{3}$ -$x^{2}$ +1)

$x^{4}$ +64

= $x^{4}$ +16 $x^{2}$ +64-16$x^{2}$

= (x^{2} +8) ² -(4x)²

= (x²+8-4x)(x²+8+4x)

$x^{5}$ + x -1

= $x^{5}$ - $x^{4}$ + $x^{3}$ + $x^{4}$ - $x^{3}$ + $x^{2}$ - $x^{2}$ + x - 1

= (x²-x+1)(x³+x²-1)

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hiep30062002

Đáp án:

`+)` `x^4+4` `=` `(x^2+2-2x)(x^2 + 2 + 2x)`

`+)` `x^5 + x + 1` `=` `( x^2 + x + 1)( x^3 - x^2 + 1)`

`+)` `a^4 + 64` `=` `(a^2 + 8-4a) (a^2 + 8+4a)`

`+)` `x^5+x-1` `=` `(x^2-x+1)(x^3+x^2-1)`

`text()`

Giải thích các bước giải:

`+)` `x^4+4`

`=` `(x^2)^2+2^2`

`=` `x^4+2.x^2 .2 + 4 -x^2`

`=` `(x^2+2)^2-(2x)^2`

`=` `(x^2+2-2x)(x^2 + 2 + 2x)`

Vậy `x^4+4` `=` `(x^2+2-2x)(x^2 + 2 + 2x)`

`+)` `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^3 - x^2 + 1)`

Vậy `x^5 + x + 1` `=` `( x^2 + x + 1)( x^3 - x^2 + 1)`

`+)` `a^4 + 64`

`=` `(a^2)^2 + 16a^2 + 64 - 16a^2`

`=` `( a^2+8)^2 - (4a)^2`

`=` `(a^2 + 8-4a) (a^2 + 8+4a)`

Vậy `a^4 + 64` `=` `(a^2 + 8-4a) (a^2 + 8+4a)`

`+)` `x^5+x-1`

`=` `x^5-x^4+x^3+x^4-x^3+x^2-x^2+x`

`=` `x^3(x^2-x+1)+x^2(x^2-x+1)-(x^2-x+1)`

`=` `(x^2-x+1)(x^3+x^2-1)`

Vậy `x^5+x-1` `=` `(x^2-x+1)(x^3+x^2-1)`

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