If the HCF of x3 – 343 and x2 – 9x + 14 and (x – 7), then find t

1.	If the HCF of x3 – 343 and x2 – 9x + 14 and (x – 7), then find their LCM.
Answer» x³ - 343 = x³ - (7)³ = (x - 7)(x² + 7x + 49) x² - 9x + 14 = x² - 2x -7x + 14 = x(x - 2) - 7(x - 2) = (x - 7)(x - 2) HCF of the polynomials = (x – 7) ∴ Reqd. LCM = \(\frac{(x^3 -343)\times(x^2-9x+14)}{HCF}\) = \(\frac{(x-7)(x^2+7x+49)\times(x-7)(x-2)}{(x-7)}\) = (x - 7)(x - 2) x (x² + 7x + 49)

If the HCF of x3 – 343 and x2 – 9x + 14 and (x – 7), then find their LCM.

Answer»

x³ - 343 = x³ - (7)³ = (x - 7)(x² + 7x + 49)

x² - 9x + 14 = x² - 2x -7x + 14

= x(x - 2) - 7(x - 2) = (x - 7)(x - 2)

HCF of the polynomials = (x – 7)

∴ Reqd. LCM = \(\frac{(x^3 -343)\times(x^2-9x+14)}{HCF}\)

= \(\frac{(x-7)(x^2+7x+49)\times(x-7)(x-2)}{(x-7)}\)

= (x - 7)(x - 2) x (x² + 7x + 49)