Question

The LCM and HCF of two polynomials are respectively (2a – 5)² (a + 1) and (2a – 5). If one of the polynomials is 4a² – 20a + 25, the other one is:

(a) 4a² + 20a + 5

(b) 4a² - 25

(c) 2a² + 3a - 5

(d) 2a² - 3a - 5

Answer 1

Correct option is (d) 2a² - 3a - 5

LCM = (2a − 5)(2a − 5)(a + 1)

HCF = (2a − 5)

One polynomial = 4a² − 20a + 25

⇒ 4a² − 10a − 10a + 25

⇒ 2a(2a − 5) − 5(2a − 5)

⇒ (2a − 5)(2a − 5)

LCM × HCF = Product of two number

Let another number is x

(2a − 5)(2a − 5)(a + 1)(2a − 5) = (2a − 5)(2a − 5) × x

x = \(\frac{(2a - 5)(2a - 5) (a + 1)(2a - 5)}{(2a - 5)(2a - 5)}\)

x = (a + 1)(2a − 5)

⇒ 2a² − 3a − 5