\(1.5x^2-10xy+5y^2-20z^2\)

\(=5\left(x^2-2xy+y^2-4z^2\right)\)

\(=5\left[\left(x^2-2xy+y^2\right)-\left(2z\right)^2\right]\)

\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)

\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)

\(2.16x-5x^2-3\)

\(=-\left(5x^2-16x+3\right)\)

\(=-\left(5x^2-15x-x+3\right)\)

\(=-\left[\left(5x^2-15x\right)-\left(x-3\right)\right]\)

\(=-\left[5x\left(x-3\right)-\left(x-3\right)\right]\)

\(=-\left(x-3\right)\left(5x-1\right)\)

\(3.x^2-5x+5y-y^2\)

\(=\left(x^2-y^2\right)-\left(5x-5y\right)\)

\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-5\right)\)

\(4.3x^2-6xy+3y^2-12z^2\)

\(=3\left(x^2-2xy+y^2-4z^2\right)\)

\(=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)

\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)
\(5.x^2+4x+3\)

\(=x^2+3x+x+3\)

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

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

\(=\left(x+3\right)\left(x+1\right)\)

\(6.\left(x^2+1\right)^2-4x^2\)

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

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

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

\(7.x^2-4x-5\)

\(=x^2-5x+x-5\)

\(=\left(x^2-5x\right)-\left(x-5\right)\)

\(=x\left(x-5\right)-\left(x-5\right)\)

\(=\left(x-5\right)\left(x-1\right)\)