Question

Factorise :

x^3 + 6x^2 + 12x + 16
​

Answer 1

Step-by-step explanation:

Let p(x) = x^3 + 6x^2 + 12x + 16

=> x^3 + 6x^2 + 12x + 8 + 8

=> x^3 + 3*2x^2 + 3*2*2*x + 2^3 + 8

=> (x+2)^3 + 2^3

=> (x+2+2) [(x+2)^2 - 2(x+2) + 4]

=> (x+4) (x^2+4x+4-2x-4+4)

=> (x+4) (x^2+2x+4)

Please mark as brainliest answer.

Answer 2

x^3 + 6x^2 + 12x + 16

= x^3 + 6x^2 + 12x + 8 + 8

= x^3 + 2x*3x + 2*2*3x+ 2^3 + 2^3

= (x+2x) + 2^3

= ( x + 2 + 2) [ (x+2)² + 2(x+2) + 4)]

= ( x + 4 ) ( x² + 2x + 4 )