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Trả lời:
a) \(x^3+2x=x\left(x^2+2\right)\)
b) \(3x^3-12x^2=3x^2\left(x-4\right)\)
a , 3x2 + 3y2 - 6xy - 12
= 3 ( x2 + y2 - 2xy - 4 )
= 3 ( x - y )2 - 22
= 3 ( x - y + 2 ) ( x - y - 2 )
\(x^2+2x-3\)
\(=x^2-x+3x-3\)
\(=x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x+3\right)\)
\(2x^2+6x-x-3\)
\(=2x\left(x+3\right)-\left(x+3\right)\)
\(=\left(x+3\right)\left(2x-1\right)\)
a)\(x^2+2x-3=x^2+3x-x-3\)
\(=x\left(x+3\right)-\left(x+3\right)\)
\(=\left(x+3\right)\left(x-1\right)\)
b)x3-7x+6=x3-x-6x+6=x(x2-1)-6(x-1)=x(x-1)(x+1)-6(x-1)
=(x-1)[x(x+1)-6]=(x-1)(x2+x-6)=(x-1)(x2+3x-2x-6)=(x-1)[x(x+3)-2(x+3)]=(x-1)(x-2)(x+3)
c)x3-x2-x-2
=x3-2x2+x2-2x+x-2
=x2(x-2)+x(x-2)+(x-2)
=(x-2)(x2+x+1)
\(x^3-7x+6\)
\(=x^3-x^2+x^2-x-6x+6\)
\(=x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-6\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x+3\right)\)
a) \(x^4-2x^3+2x-1\)
\(=x^4-x^3-x^3+2x-2+1\)
\(=\left(x^4-x^3\right)+\left(2x-2\right)-\left(x^3-1\right)\)
\(=x^3\left(x-1\right)+2\left(x-1\right)-\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x-1\right)\left(x^3+2-x^2-x-1\right)\)
\(=\left(x-1\right)\left(x^3-x^2-x+1\right)\)
\(=\left(x-1\right)\left[\left(x^3-x^2\right)-\left(x-1\right)\right]\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x^2-1\right)\left(x-1\right)\)
\(=\left(x-1\right)^2\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)^3\left(x+1\right)\)
b) \(x^4+2x^3+2x^2+2x+1\)
\(=\left(x^4+2x^2+1\right)+\left(2x^3+2x\right)\)
\(=\left(x^2+1\right)^2+2x\left(x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^2+1+2x\right)\)
\(=\left(x^2+1\right)\left(x+1\right)^2\)
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,(x-4)(x+3)
b,(x-1)(x^2+x+3)
a/\(x^2-x-12\)
\(=x^2+3x-4x-12\)
\(=\left(x^2+3x\right)-\left(4x+12\right)\)
\(=x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x+3\right)\left(x-4\right)\)
b/ \(x^3+2x-3\)
\(=x^3+x^2-x^2+3x-x-3\)
\(=\left(x^3-x^2\right)+\left(3x-3\right)+\left(x^2-x\right)\)
\(=x^2\left(x-1\right)+3\left(x-1\right)+x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+3+x\right)\)