a/ $a^2x-a^2y+ax-ay-x+y\\=(a^2x-a^2y)+(ax-ay)-(x-y)\\=a^2(x-y)+a(x-y)-(x-y)\\=(a^2+a-1)(x-y)\\=\left(a^2+2.a.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{5}{4}\right)(x-y)\\=\left[\left(a+\dfrac{1}{2}\right)^2-\left(\dfrac{\sqrt 5}{2}\right)^2\right](x-y)\\=\left(a+\dfrac{1}{2}-\dfrac{\sqrt 5}{2}\right)\left(a+\dfrac{1}{2}+\dfrac{\sqrt 5}{2}\right)^2(x-y)\\=\left(a+\dfrac{1-\sqrt 5}{2}\right)\left(a+\dfrac{1+\sqrt 5}{2}\right)(x-y)$
b/ $x^2-6xy+9y^2-x+3y\\=(x^2-6xy+9y^2)-(x-3y)\\=(x-3y)^2-(x-3y)\\=(x-3y)(x-3y-1)$
c/ $x^2+x-12\\=x^2+4x-3x-12\\=(x^2+4x)-(3x+12)\\=x(x+4)-3(x+4)\\=(x-3)(x+4)$
