Factorisation

Question

How to factorise

 

x³ + ax² + a²x - b³ = 0

Answer 1

Hi Gautam,

 

x^3 + ax^2 + a^2x - b^3 = 0

rewrite as

ax^2 + a^2x + x^3 - b^3 = 0

ax(x+a) + x^3 - b^3 = 0 

x^3 - b^3 is the difference of two cubes and can be factored as

x^3 - b^3 = (x-b)(x^2+xb+b^2)

then, the final form is

ax(x+a) + (x-b)(x^2+xb+b^2) = 0