Question

Plz answer me the topmost one

Answer 1

hope you like the answer.

Answer 2

Answer:

(x + 1)(x - 1)(x² + 1)

Step-by-step explanation:

Given polynomial are:

⇒ x³ + x² + x + 1 and x⁴ - 1

(i)

Factors of x³ + x² + x + 1

= (x³ + 1) + (x² + x)

= (x³ + 1) + x(x + 1)

We know that a³ + b³ = (a + b)(a² - ab + b²)

= (x + 1)(x² - x + 1) + x(x + 1)

= (x + 1)[x² - x + 1 ) + x]

= (x + 1)[x² - x + 1 + x]

= (x + 1)(x² + 1).

(ii)

Factors of x⁴ - 1.

= (x²)² - (1)²

We know that a² - b² = (a + b)(a - b)

= (x² + 1)(x² - 1)

= (x² + 1)(x + 1)(x - 1).

Now,

LCM of x³ + x² + x + 1 and x⁴ - 1.

⇒ (x + 1)(x² + 1)(x - 1).