a) \(16\text{x}-5\text{x}^2-3\)
\(=-5\text{x}^2+15\text{x}+x-3\)
\(=-5\text{x}\left(x-3\right)+\left(x-3\right)\)
\(=\left(x-3\right)\left(-5\text{x}+1\right)\)
b) \(x^8+3x^4+4\)
\(=\left(x^8+4\text{x}^4+4\right)-x^4\)
\(=\left(x^4+2\right)^2-x^4\)
\(=\left(x^4-x^2+2\right)\left(x^4+x^2+2\right)\)
c) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(=\left(x^2+x+1\right)\text{[}\left(x^2+x+1\right)+1\text{]}-12\)
\(=\left(x^2+x+1\right)^2+\left(x^2+x+1\right)-12\)
\(=\left(x^2+x+1\right)^2-3\left(x^2+x+1\right)+4\left(x^2+x+1\right)-12\)
\(=\left(x^2+x+1\right)\left(x^2+x-2\right)+4\left(x^2+x-2\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
