Question

factorize x^3+3x^2+3x-7​

Answer 1

Answer:

(x + 1)(x^2 - 4x + 7)

Step-by-step explanation:

We have,

x^3 - 3x^2 + 3x + 7

= x^3 - 3x^2 + 3x - 1 + 8

= {x^3 - 3x^2 + 3x - 1} + (2)^3

= {x^3 - 1 - 3x^2 + 3x} + (2)^3

= {(x)^3 - (1)^3 - 3(x)^2 × 1 + 3 × x × (1)^2} + (2)^3 [a^3 - b^3 - 3a^2b + 3ab^2 = (a-b)^3 ]

= (x - 1)^3 + (2)^3

= (x - 1 + 2){(x - 1)^2 - (x - 1)•(2) + (2)^2}

= (x + 1)(x^2 - 2x + 1 - 2x + 2 + 4)

= (x + 1)(x^2 - 4x + 7)