Factor the Two Polynomials

Question

Factor completely:

 

1. x²–xy+x–xy²+y³–y²
2. x²y+x+xy²+y+2xy+2

Answer 1

(1)

 

x² – xy + x – xy² + y³ – y² = x(x - y +1) + y²(-x + y - 1)

 

= x(x - y +1) - y²(x - y + 1) = (x - y²)(x - y + 1)

 

(2)

 

x²y + x + xy² + y+ 2xy + 2 = x(xy + 1) + y(xy + 1) + 2(xy + 1)

 

= (x + y + 2)(xy + 1)