h) \(x^4+4=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)

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

x^4+4=x^4+4x^2+4-4x^2=(x^2+2)^2-(2x)^2=(x^2+2-2x)(x^2+2+2x)

a) \(x-2-3\left(x-1\right)\left(x-2\right)=0\)

\(=-3x^2+10x+8=0\)

\(\Rightarrow x=\frac{4}{3};x=2\)

f) \(x^2-6x+5=\left(x^2-x\right)+\left(-5x+5\right)=x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(x-5\right)\)

g) \(x^4+64=\left(x^2+4x+8\right)\left(x^2-4x+8\right)\)

\(x^2-6x+5\)

\(=\left(x^2-2.3x+3^2\right)-4\)

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

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

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

d)  \(2x^2-3x-27\)

\(=\left(2x^2+6x\right)-\left(9x+27\right)\)

\(=2x\left(x+3\right)-9\left(x+3\right)\)

\(=\left(2x-9\right)\left(x+3\right)\)

e)  \(2x^2-5xy-3y^2\)

\(=\left(2x^2+xy\right)-\left(6xy+3y^2\right)\)

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

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

b/ (x + 1)(x + 5)

c/ (x - 5)(x - 2)

\(b,x^2+6x+5=x^2+x+5x+5=x\left(x+1\right)+5\left(x+1\right)=\left(x+1\right)\left(x+5\right)\)

\(c,x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)=\left(x-2\right)\left(x-5\right)\)