Question

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Answer 1

Solution 1:

Given Polynomial:

= 4x⁴ + 8x² + 9

Can be written as:

= 4x⁴ + (12 - 4)x² + 9

= 4x⁴ + 12x² - 4x² + 9

= 4x⁴ + 12x² + 9 - 4x²

= (2x²)² + 2 × (2x²) × (3) + (3)² - 4x²

Using identity a² + 2ab + b² = (a + b)², we can write:

= (2x² + 3)² - 4x²

= (2x² + 3)² - (2x)²

Using identity a² - b² = (a + b)(a - b), we get:

= (2x² + 2x + 3)(2x² - 2x + 3)

★ Therefore, the factorised form of the polynomial is (2x² + 2x + 3)(2x² - 2x + 3)

Solution 2:

Given Polynomial:

= x⁴ + x² + 1

Can be written as:

= x⁴ + (2 - 1)x² + 1

= x⁴ + 2x² - x² + 1

= x⁴ + 2x² + 1 - x²

= (x²)² + 2 × (x²) × 1 + (1)² - x²

Using identity a² + 2ab + b² = (a + b)², we can write:

= (x² + 1)² - x²

= (x² + 1)² - (x)²

Using identity a² - b² = (a + b)(a - b), we get:

= (x² + x + 1)(x² - x + 1)

★ Therefore, the factorised form of the polynomial is (x² + x + 1)(x² - x + 1)

Answers:

• (2x² + 2x + 3)(2x² - 2x + 3)
• (x² + x + 1)(x² - x + 1)

Answer 2

refer the given attachment