Question

The product of two expression is \(x^3 + x^2 - 44x - 84\). If the HCF of these two expressions is x + 6, then their LCM will be:

(a) (x + 2)(x + 7)

(b) (x + 2)(x - 7)

(c) (x - 2)(x + 7)

(d) (x - 2)(x - 7)

Answer 1

(b) (x - 7)(x + 2)

LCM × HCF = Product of the expressions

⇒ LCM = \(\frac{\text{Prod. of expressions}}{HCF}\)

= \(\frac{x^+x^2-44x-84}{(x+6)}\)

Performing long division, we have

∴ Reqd. LCM = x² - 5x - 14 = (x - 7)(x + 2)