Question

The factors of x square + 4 y square + 4y - 4xy - 2x minus 8 are

Answer 1

Let the given polynomial be the product of :

(x + b y + c) ( x + 4/b y - 8/c) Expand that:

x^2 + (4/b + b) x y + (c - 8 /c) x + 4 y^2 + (4c/b - 8 b/c) y - 8compare coefficients and equate them:

4 + b^2 + 4 b= 0 .... 1

c^2 - 8 + 2 c = 0 .....2

c^2 - 2 b^2 - bc = 0 ..... 3

Solving them , easily: b = - 2 c = 2 or - 4

Factors are :

x^2 + 4 y^2 + 4 y - 4 x y - 2 x - 8

= (x -2 y + 2 ) (x -2 y - 4) OR (x -2 y - 4) (x -2 y + 2 ).