\(13,x^2-x-3x+3\\ =x\left(x-1\right)-3\left(x-1\right)\\ =\left(x-3\right)\left(x-1\right)\\ ---\\ 16,x^3-3x^2-4x+12\\ =x^2\left(x-3\right)-4\left(x-3\right)\\ =\left(x-3\right)\left(x^2-4\right)\\ =\left(x-3\right)\left(x-2\right)\left(x+2\right)\\ ---\\ 15,x^2-2x-3x+6\\ =x\left(x-2\right)-3\left(x-2\right)\\ =\left(x-3\right)\left(x-2\right)\\ ---\\ 14,x^2+x+3x+3\\ =x\left(x+1\right)+3\left(x+1\right)\\ =\left(x+3\right)\left(x+1\right)\\ ---\\ 17,45+x^3-5x^2-9x\\ =x^2\left(x-5\right)-9\left(x-5\right)\\ =\left(x^2-9\right)\left(x-5\right)\\ =\left(x-3\right)\left(x+3\right)\left(x-5\right)\\ ---\\ 18,x^5+x^4+x+1\\ =x^4\left(x+1\right)+\left(x+1\right)\\ =\left(x^4+1\right)\left(x+1\right)\)
\(26,3x^2-3xy-5x+5y\\ =3x\left(x-y\right)+5\left(x-y\right)\\ =\left(3x+5\right)\left(x-y\right)\\ ---\\ 27,xz+yz-5x-5y\\ =z\left(x+y\right)-5\left(x+y\right)\\ =\left(z-5\right)\left(x+y\right)\\ ----\\ 21,x^5+x^4+x+1\\ =x^4\left(x+1\right)+\left(x+1\right)\\ =\left(x^4+1\right)\left(x+1\right)\\ ---\\ 24,ax+ay+bx+by\\ =a\left(x+y\right)+b\left(x+y\right)\\ =\left(a+b\right)\left(x+y\right)\\ ---\\ 27,5a^2-5ax-7a+7x\\ =5a\left(a-x\right)-7\left(a-x\right)\\ =\left(5a-7\right)\left(a-x\right)\\ ---\\ 30,3x^2-3xy-5x+5y\\ =3x\left(x-y\right)-5\left(x-y\right)\\ =\left(3x-5\right)\left(x-y\right)\)
\(19,x^4-9x^3+x^2-9x\\ =x^3\left(x-9\right)+x\left(x-9\right)\\ =\left(x^3+x\right)\left(x-9\right)\\ =x\left(x^2+1\right)\left(x-9\right)\\ ---\\ 22,x^3+x^2+x+1\\ =x^2\left(x+1\right)+\left(x+1\right)\\ =\left(x^2+1\right)\left(x+1\right)\\ ---\\ 25,x^2-xy+x-y\\ =x\left(x-y\right)+\left(x-y\right)\\ =\left(x-y\right)\left(x+1\right)\\ ---\\ 20,x^3+x^2+x+1\\ =x^2\left(x+1\right)+\left(x+1\right)\\ =\left(x+1\right)\left(x^2+1\right)\\ ---\\ 28,x^2-xy+x-y\\ =x\left(x-y\right)+\left(x-y\right)\\ =\left(x+1\right)\left(x-y\right)\\ ---\\ 23,x^3+7x^2-4x-28\\ =x^2\left(x+7\right)-4\left(x+7\right)\\ =\left(x^2-4\right)\left(x+7\right)\\ =\left(x-2\right)\left(x+2\right)\left(x+7\right)\)
24: ax+ay+bx+by
=(ax+ay)+(bx+by)
=a(x+y)+b(x+y)
=(x+y)(a+b)
25: \(x^2-xy+x-y\)
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
26: \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
27: \(5a^2-5ax-7a+7x\)
\(=\left(5a^2-5ax\right)-\left(7a-7x\right)\)
\(=5a\left(a-x\right)-7\left(a-x\right)\)
\(=\left(a-x\right)\left(5a-7\right)\)
28: \(x^2-xy+x-y\)
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
29: \(xz+yz-5x-5y\)
\(=\left(xz+yz\right)-\left(5x+5y\right)\)
\(=z\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(z-5\right)\)
30: \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)