From (x 1) as factor x = 1 X³ - k = 0 or 1 - k = 0   k = 1

x + 2 is a factor             x = - 2 makes it zero

(-2)³ + 6(-2)² + 4(-2) + k = 0       i.e k = - 8

HCF is common term with lowest power

t² - 4t + 1 = 0   or t² + 1 = 4t                 t + 1/t = 4         Or (t + 1/t + 3 (t + 1/t) = 64 or t³ + 1/t³ = 64 - 3 x 4 = 52

(x + 1/x) = 3    (x + 1/x)² = 9     Or  x² + 1/x² + 2 = 9          x² + 1/x² = 7

x³ + x² + x + 1 = (x² + 1) (x + 1) and x⁴ - 1 = (x - 1) (x + 1) (x² + 1) H.C.F. = (x + 1) (x² + 1)

 L.C.M of 2, 3, 5 = 30

(x + 1) (x² - x + 1) = (x³ + 1) and hence LCM of terms

Factor of 28 which is also factor of other two terms.

LCM of numerators divided by GCD of denominators:  LCM of numerators is 6. HCF of denominators is 5. So, the LCM of given terms is 6/5.

LCM is highest power of all the factors There is only 1 factor (a+b) with its highest power  13 

Make factors and find HCF

a³ + b³ = (a + b) (a² - ab + b²) and a⁴ - b⁴ = (a - b) (a + b) (a² + b²)

HCF = a + b Hence, LCM = (a³ + b³) (a - b) (a + b) (a² + b²) / (a + b) = (a³ + b³) (a - b) (a² + b²)

Area A = 8x² - 2x - 15 = (2x - 3) (4x + 5)  or Length = (4x + 5) units as length is greater than the breadth  

x² - 4x - 12 = (x - 6 )(x + 2) and second expression is (x + 2)² (x - 2).

L.C.M = (x - 6) (x - 2) (x + 2)²

H.C.F of 10, 15 and 25 and common term with least power

L.C.M is common term with highest power and all other terms

If highest number is divisible be other two then that is LCM.

15 or multiple of 105 which are multiple of other two terms

If lowest term is factor of the other term, then that is HCF of all.

(x - 1) (x² + x + 1) = (x³ -1) and hence LCM of terms

Factors of 90 = 2 x 3 x 3 x 5 Factors of 225 = 5 x 5 x 3 x 3   H.C.F of 90 and 225 = 3 x 5 x 3 = 45

H.C.F of numerator is divided by L.C.M of denominator = 2/63 

GCD is common term with lowest power

The required LCM is 24x²y².