Question

Match each polynomial with its factorisation. 1. x² + 2x - 15

Factorization: (x - 3)(x + 3)(x²+ 9)

2. 2x²
Factorization: 2(x-4)(x+4)

3. x⁴ - 8 ]
Factorization: (x - 8)

4. x² - 16x + 64
Factorization: (+3) (7-x)

5. - x² + 4x + 2 ]
Factorization: (1-5x) (x+2)

6. 4 - 9x - 2 - 5x²
Factorization: (+5) (x-3)

Answer 1

The polynomial factorizations are x² + 2x - 15: (x - 3)(x + 5), 2x²: 2(x²), x⁴ - 8: (x² + 2)(x² - 2), x² - 16x + 64: (x - 8)(x - 8), -x² + 4x + 2: No factorization, 4 - 9x - 2 - 5x²: No factorization.

Step-by-step explanation:

The correct match between the given polynomials and their factorizations is:

x² + 2x - 15: Factorization: (x - 3)(x + 5)

2x²: Factorization: 2(x²)

x⁴ - 8: Factorization: (x² + 2)(x² - 2)

x² - 16x + 64: Factorization: (x - 8)(x - 8)

-x² + 4x + 2: The given polynomial cannot be factorized.

4 - 9x - 2 - 5x²: The given polynomial cannot be factorized.

Only the first four polynomials have valid factorizations. The fifth and sixth polynomials cannot be factorized further.