a) \(x^4+x^3+2x^2+x+1\)

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

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

c) \(\left(x^3-27\right)-4x\left(x-3\right)=\left(x-3\right)\left(x^2-x+9\right)\)

a) \(2x\left(x-7\right)+5\left(x-7\right)=0\)

\(\Leftrightarrow\left(2x+5\right)\left(x-7\right)=0\)

\(\Leftrightarrow x=\frac{-5}{2},x=7\)

b) \(x^3-2x^2+x-2=0\)

\(\Leftrightarrow x^2\left(x-2\right)+\left(x-2\right)=0\)

\(=\left(x^2+1\right)\left(x-2\right)=0\)

Vậy x = 2

\(x^2-12x=36\)

\(\Leftrightarrow\left(x-6\right)^2=72\)

\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{72}+6\\x=6-\sqrt{72}\end{cases}}\)

a) \(ax^3-3ax^2+3ax-a\)

\(=a\left(x^3-1\right)-3ax\left(x-1\right)\)

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

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

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

\(x^2-a^2+2ab-b^2\)

\(=x^2-\left(a-b\right)^2\)

\(=\left(x-a+b\right)\left(x+a-b\right)\)

\(x^2-x-y^2-y\)

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

\(=\left(x+y\right)\left(x-y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y-1\right)\)

\(x^2-2xy+y^2-z^2\)

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

\(=\left(x-y-z\right)\left(x-y+z\right)\)

a) \(xy+y^2+x+y\)

\(=y\left(x+y\right)+\left(x+y\right)\)

\(=\left(y+1\right)\left(x+y\right)\)

b) \(x^2-3x+xy-3y\)

\(=x\left(x-3\right)+y\left(x-3\right)\)

\(=\left(x+y\right)\left(x-3\right)\)

c) \(x^3-2x^2-3x+6\)

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

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

d) \(x^2+2xy+6y-9\)

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

chịu luôn

\(x^2\left(x-3\right)-4x+12\)

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

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

\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)=0\)