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1/ x3 + x2y - x2z -xyz
= x2(x + y) - xz(x + y)
= (x + y) (x2 - xz)
= x (x + y) (x - z)
2/ 3x3y - 18x2y2 + 27xy3
= 3xy(x2 - 6xy + y2)

a) \(x^2yz+4zyx+4yz\)
\(=yz\left(x^2+4x+4\right)\)
\(=yz\left(x+2\right)^2\)
b) \(5x^4-3x^3y-45x^2y^2+27xy^3\)
\(=x\left(5x^3-3x^2y-45xy^2+27y^3\right)\)

a: Ta có: \(10x^4-27x^3y-110x^2y^2-27xy^3+10y^4\)
\(=10x^4+20x^2y^2+10y^4-27xy\left(x^2+y^2\right)-130x^2y^2\)
\(=10\left(x^2+y^2\right)^2-27xy\left(x^2+y^2\right)-130x^2y^2\)
\(=10\left(x^2+y^2\right)^2-52xy\left(x^2+y^2\right)+25xy\left(x^2+y^2\right)-130x^2y^2\)
\(=2\left(x^2+y^2\right)\left(5x^2+5y^2-26xy\right)+5xy\left(5x^2+5y^2-26xy\right)\)
\(=\left(5x^2-26xy+5y^2\right)\left(2x^2+5xy+2y^2\right)\)
\(=\left(5x^2-25xy-xy+5y^2\right)\left(2x^2+4xy+xy+2y^2\right)\)
\(=\left\lbrack5x\left(x-5y\right)-y\left(x-5y\right)\right\rbrack\left\lbrack2x\left(x+2y\right)+y\left(x+2y\right)\right\rbrack\)
=(5x-y)(x-5y)(2x+y)(x+2y)
b: \(x^5-4x^4+3x^3+3x^2-4x+1\)
\(=x^5+x^4-5x^4-5x^3+8x^3+8x^2-5x^2-5x+x+1\)
\(=\left(x+1\right)\left(x^4-5x^3+8x^2-5x+1\right)\)
\(=\left(x+1\right)\left(x^4-x^3-4x^3+4x^2+4x^2-4x-x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(x^3-4x^2+4x-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left\lbrack\left(x^3-x^2\right)-3x^2+3x+x-1\right\rbrack\)
\(=\left(x+1\right)\left(x-1\right)\cdot\left(x-1\right)\left(x^2-3x+1\right)=\left(x+1\right)\left(x-1\right)^2\cdot\left(x^2-3x+1\right)\)

\(3y^3+6xy^2+3x^2y=3y\left(y^2+2xy+x^2\right)=3y\left(x+y\right)^2\)
\(x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(x^3+3x^2-3x-1=\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)=\left(x-1\right)\left(x^2+x+1+3x\right)\)
\(=\left(x-1\right)\left(x^2+4x+1\right)\)
Tham khảo nhé~

\(3x^4-5x^3-18x^2-3x+5.\)
\(=3x^4-6x^3+x^3-15x^2-2x^2-x^2-5x+2x+5\)
\(=3x^4-6x^3-15x^2+x^3-2x^2-5x-x^2+2x+5\)
\(=\left(3x^4-6x^3-15x^2\right)+\left(x^3-2x^2-5x\right)-\left(x^2-2x-5\right)\)
\(=3x^2\left(x^2-2x-5\right)+x\left(x^2-2x-5\right)-\left(x^2-2x-5\right)\)
\(=\left(x^2-2x-5\right)\left(3x^2+x-1\right)\)

Phân tích đa thức thành nhân tử:
\(3x^2-12x^2y^2+3y^2+6xy\)
\(=3\left(x^2-4x^2y^2+y^2+2xy\right)\)
\(=3\left[\left(x^2+2xy+y^2\right)-\left(2xy\right)^2\right]\)
\(=3\left[\left(x+y\right)^2-\left(2xy\right)^2\right]\)
\(=3\left(x+y-2xy\right)\left(x+y+2xy\right)\)
3x(\(^{x^2-6xy+9y^2}\))
3x\(\left(x-3y\right)^2\)