\(a)x^2-5x-14=x^2-7x+2x-14\)
\(=x\left(x-7\right)+2\left(x-7\right)\)
\(=\left(x-7\right)\left(x+2\right)\)
\(b)4x^2-3x-1=4x^2-3x-4+3\)
\(=4\left(x^2-1\right)-3\left(x-1\right)\)
\(=4\left(x+1\right)\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(4-3\right)\left(x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)\)
\(c)x^4+64=x^4+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+4x+8\right)\left(x^2-4x+8\right)\)