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a, x2-7x-14y+2x
=x(x+2)-7(x-2y)
b, x3-4x2y+4xy2-25x
=x3-4x2y+4xy2-y3-25x+y3
=(x-y)3-25x+y3
a ) = x(x+2) - 7(x+2y)
b) = -4 xy ( x-y) + (x^3-25x) [ câu này mk , chaqcs là làm đúng đâu ]
a)2(x-3)+12-4x
=x2(x-3)-4(x-3)
=(x2-4)(x-3)
=(x2-22)(x-3)
=(x+2)(x-2)(x-3)
b)x3-4x2-12x+27
=x3-7x2+9x+3x2-21x+27
=x(x2-7x+9)+3(x2-7x+9)
=(x+3)(x2-7x+9)
a)\(x^2\left(x-3\right)+12-4x\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-2^2\right)\left(x-3\right)\)
\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)\)
Với x = -3 ta có -27-4*9+ 36+27=0 do đó đa thức chứa nhân tử x+3
Ta có: x^3 -4x^2-12x+27 = x^3 +3x^2 -7x^2-21x+9x+27 =(x^3 +3x^2)-(7x^2+21x) + (9x+27) =x^2(x+3) -7x(x+3)+ 9(x+3)=(x+3)(X^2 - 7x+9)
* Xét x^2 -7x + 9 = x^2 - 2x.7/2 +49/4-49/4+9 = (x-7/2)^2 -13/4 =(x-7/2- √13/2)(x-7/2+√13/2)
Vậy: x^3 -4x^2-12x+27 = (x+3)(x-7/2)^2 -13/4 =(x-7/2- √13/2)(x-7/2+√13/2)
k cho mình nha
câu a đặt chung x ra là xong
câu b
x^3 + 3x^2 - 7x^2 - 21x + 9x+ 27 còn lại tự làm nhé
a) x3 - 2x2 + x - xy2
= x (x2 - 2x + 1 - y2)
= x [(x2 - 2x + 1) - y2]
= x [(x - 1)2 - y2]
= x [(x - 1) + y] [(x - 1) - y]
= x (x - 1 + y) (x - 1 - y)
b) x3 - 4x2 - 12x + 27
= (x3 + 27) - (4x2 + 12x)
= (x3 + 33) - 4x (x + 3)
= (x + 3) (x2 - 3x + 32) - 4x (x + 3)
= (x + 3) [(x2 - 3x + 9) - 4x]
= (x + 3) (x2 - 3x + 9 - 4x)
= (x + 3) (x2 - 7x + 9)
#Học tôt!!!
~NTTH~
a) = (x3 +33) -4x(x+3)
= (x+3)(x2 -3x+9-4x)
= (x+3)(x2 - 7x +9)
a) x2 – 4 + (x – 2)2
= (x2 – 22) + (x – 2)2 = (x – 2)(x + 2) + (x – 2)2
= (x – 2) [(x + 2) + (x – 2)]
= (x – 2)(x + 2 + x – 2)
= 2x(x – 2)
b) x3 – 2x2 + x – xy2
= x(x2 – 2x + 1 – y2) = x[(x2 – 2x + 1) – y2]
= x[(x – 1)2 – y2]
= x[(x – 1) + y] [(x – 1) – y]
= x(x – 1 + y)(x – 1 – y)
c) x3 – 4x2 – 12x + 27
= (x3 + 27) – 4x(x + 3)
= (x + 3)(x2 – 3x + 9) – 4x(x + 3)
= (x + 3)(x2 – 3x + 9 – 4x)
= (x + 3)(x2 – 7x + 9)
\(x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+2x\right)=\left(x+1\right)\left(x^2+x+1\right)\)
\(x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27\)
\(=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
\(x^4+2x^3+2x^2+2x+1=x^4+x^2+2x^3+x^2+2x+1\)
\(=x^2\left(x^2+1\right)+2x\left(x^2+1\right)+\left(x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^2+2x+1\right)\)
\(=\left(x^2+1\right)\left(x+1\right)^2\)
\(x^4-2x^3+2x-1=\left(x^4-1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+1-2x\right)=\left(x^2-1\right)\left(x-1\right)^2\)
\(x^3+2x^2+2x+1=\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)\)
\(=x^2.\left(x+1\right)+x.\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2+x+1\right)\)
\(x^3-4x^2+12x-27\)
\(=\left(x^3-x^2\right)-\left(3x^2-3x\right)+\left(9x-27\right)\)
\(=x^2.\left(x-1\right)-3x.\left(x-1\right)+9.\left(x-3\right)\)
\(=\left(x-1\right).\left(x^2-3x\right)+9.\left(x-3\right)\)
\(=x.\left(x-1\right).\left(x-3\right)+9.\left(x-3\right)\)
\(=\left(x-3\right)\left[x.\left(x-1\right)+9\right]\)
\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\\ =\left(x+3\right)\left(x^2-3x+9-4x\right)=\left(x+3\right)\left(x^2-7x+9\right)\)
\(x^3-4x^2-12x+27\)
\(=x^3+3x^2-7x^2-21x+9x+27\)
\(=x^2\left(x+3\right)-7x\left(x+3\right)+9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)