\(2x^3+x^2+2x+1=x^2\left(2x+1\right)+2x+1=\left(2x+1\right)\left(x^2+1\right)\)
\(x^3-5x^2+5x-20=x^2\left(x-5\right)+5\left(x-5\right)=\left(x-5\right)\left(x^2+5\right)\)
\(3x^4-x^3-6x+2=x^3\left(3x-1\right)-2\left(3x-1\right)=\left(3x-1\right)\left(x^3-2\right)\)
\(x^3y+x^2y^2-4x-4y=x^2y\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(x^2y-4\right)\)
\(x^2-4y^2+3x+6y=\left(x-2y\right)\left(x+2y\right)+3\left(x+2y\right)=\left(x+2y\right)\left(x-2y+3\right)\)
\(x^2-4xy+4y^2-81=\left(x-2y\right)^2-9^2=\left(x-2y-9\right)\left(x-2y+9\right)\)
\(x^2-25+2xy+y^2=\left(x+y\right)^2-5^2=\left(x+y+5\right)\left(x+y-5\right)\)
\(15x+4-9x^2-10=5\left(3x-2\right)-\left(3x-2\right)\left(3x+2\right)=\left(3x-2\right)\left(3-3x\right)=3\left(3x-1\right)\left(1-x\right)\)
\(ax^2+ay-bx^2-by=\left(a-b\right)x^2+\left(a-b\right)y=\left(a-b\right)\left(x^2+y\right)\)
