Question

Factorise x^4 + 1 + x^2.

Answer 1

To find :- Factorise the expression.

Solution :-

we know that,

factorization is the process of breaking expression to make a single term that, multiplied together, give us that original expression.

→ x⁴ + 1 + x²

→ x⁴ + 2x² + 1 - x²

using the factoring formula a² + 2ab + b² = (a + b)²,

→ (x² + 1²) - x²

using the factoring formula a² - b² = (a + b) (a - b),

→ ((x² + 1) + x) ((x² + 1) - x)

→ ((x² + 1) + x) (x² - x + 1)

→ (x² + x + 1) (x² - x + 1)

→ (x² - x + 1) (x² + x + 1)

Hence, the factorisation of x^4 + 1 + x^2 is (x² - x + 1) (x² + x + 1).

Answer 2

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