a, 16x^{4}+4=16x^{4}+16x^{2}+4-16x^{2}=(4x+2)^{2}-16x^{2}=(8x+2).4=8(4x+1)
b, x^{5}+x+1=x^{5}+x^{4}+x^{3}-x^{4}-x^{3}-x^{2}+x^{2}+x+1=x^{3}(x^{2}+x+1)-x^{2}(x^{2}+x+1)+(x^{2}+x+1)=(x^{3}-x^{2}+1)(x^{2}+x+1)
c,a(b^{2}-c^{2})+b(c^{2}-a^{2})+c(a^{2}-b^{2})
=(ab+ac)(b-c)+(bc+ba)(c-a)+(ca+cb)(a-b)...