Verified answer

3x^3+x^2+3x+1=3x(x^2+1)+(x^2+1)=(x^2+1)((3x+1)

2x+2y-x^2-xy=2(x+y)-x(x+y)=(x+y)(2-x)

x^7+9x^6-x^2-9x=x^6(x+9)-x(x+9)=(x+9)(x^6-x)=x(x^5-1)(x+9)=x(x+9)(x-1)(x^4+x^3+x^2+x+1)

(a+b)^2+2a+2b=(a+b)^2+2(a+b)=(a+b)(a+b+2)