The expression x4 + 4 can be factorized as: - Vidyadip

MCQ

The expression x⁴ + 4 can be factorized as:

A
(x² - 2x - 2) (x² - 2x + 2)
B
(x² + 2) (x² -2)
C
(x² + 2x + 2) (x² + 2x - 2)
D
(x² + 2x + 2) (x² - 2x + 2)

✓

Answer

(x² + 2x + 2) (x² - 2x + 2)
Solution:
The given expression to be factorized is x⁴ + 4
This can be written in the form
x⁴ + 4 = (x²)² + (2)² + 4x² - 4x²= {(x²)² + 2 × x² × 2 + (2)²} - (2x)²= (x² + 2)² - (2x)²= (x² + 2 + 2x) (x² + 2 - 2x)

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