\(A=x^3-15x^4+16x^3-29x^2\)

\(A=\left(x^3+16x^3\right)-15x^4-29x^2\)

\(A=17x^3-15x^4-29x^2\)

\(A=-15x^4+17x^3-29x^2\)

\(A=-x^2\left(15x^2-17x+29\right)\)

\(x^3-6x^2y+12xy^2-8y^3\)

\(=\left(x-2y\right)^3\)

bạn ơi  bạn viết sai đề có đề nào viết  thế này đâu?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Uchiha Itachi

\(x^5+x^4+x^3+x^2+x+1\)

\(=\left(x^5+x^4+x^3\right)+\left(x^2+x+1\right)\)

\(=x^3\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^3+1\right)\left(x^2+x+1\right)\)

\(=\left(x+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

Ta có: \(x^5+x^4+x^3+x^2+x+1\)

\(=x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)\)

\(=\left(x+1\right)\left(x^4+x^2+1\right)\)

\(=\left(x+1\right)\left(x^4+2x^2+1-x^2\right)\)

\(=\left(x+1\right)\left\lbrack\left(x^2+1\right)^2-x^2\right\rbrack=\left(x+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

\(-8x^3+1=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)

\(=\left(x+y+z\right)\left\lbrack\left(x+y\right)^2-z\left(x+y\right)+z^2\right\rbrack-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-zx-zy+z^2-3xy\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)\)

2.\(\left(x^2-16y^2\right)-3x+12y=\left(x-4y\right)\left(x+4y\right)-3\left(x-4y\right)=\left(x-4y\right)\left(x+4y-3\right)\)

4.\(x^3+6x^2+12x+8=\left(x+2\right)^3\)

Trả lời:

a, x⁴ + 3x³ + x² + 3x

= ( x⁴ + 3x³ ) + ( x² + 3x )

= x³ ( x + 3 ) + x ( x + 3 )

= ( x³ + x ) ( x + 3 )

= x ( x² + 1 ) ( x + 3 )

b, Sửa đề: x⁴ - x² + 8x - 8

= ( x⁴ - x² ) + ( 8x - 8 )

= x² ( x² - 1 ) + 8 ( x - 1 ) 

= x² ( x - 1 ) ( x + 1 ) + 8 ( x - 1 )

= ( x - 1 ) [ x² ( x + 1 ) + 8 ]

= ( x - 1 ) ( x³ + x² + 8 )

x⁴ + 3x³ + x² + 3x = x³(x + 3) + x(x + 3)
= (x + 3)(x² + 1)x

6, x mũ 4 - 4x mũ 3 - 8x mũ 2 + 8x =x (x+2) (x^2-6x+4)

8, x mũ 4 + 2x mũ 3 + x mũ 2 - y mũ 2  = -(y-x^2-x) (y+x^2+x)

10, 4x mũ 2 ( x + y ) -x - y  = (2x-1) (2x+1) (y+x)