Question

The positive square root of (2x² + 5x + 2) (x² - 4) (2x² - 3x - 2) expressed as factors is:

(a) (2x + 3) (x + 2) (x - 1)

(b) (x + 2) (x - 2) (2x - 1)

(c) (2x + 1) (x + 2) (x - 2)

(d) (2x + 1) (x - 2) (x - 1)

Answer 1

Correct option is (c) (2x + 1) (x + 2) (x - 2)

(2x² + 5x + 2)(x² − 4)(2x² − 3x − 2)

⇒ (2x² + x + 4x + 2)(x + 2)(x − 2)(2x² − 3x − 2)

⇒ [x(2x + 1) + 2(2x + 1)] [(x + 2)(x − 2)] [x(2x + 1) − 2(2x + 1)]

⇒ [(2x + 1)(x + 2)] [(x + 2)(x − 2)] [(2x + 1)(x − 2)]

⇒ (2x + 1)² (x + 2)² (x − 2)²

So, Required square root is (2x + 1) (x + 2) (x − 2).