Question

find the h.c.f of (a2-a)(a+1)​

Answer 1

Answer:

Problem 1 :

Find the LCM of the following polynomials whose GCD is (a - 2).

(a2 + 4a −12) and (a2 −5a + 6)

Solution :

Let f(x) = a2 + 4a −12, g(x) = a2 −5a + 6.

f(x) = a2 + 4a −12

= a2 + 6a - 2a −12

= a(a + 6) - 2(a + 6)

f(x) = (a + 6)(a - 2)

g(x) = a2 −5a + 6

= a2 - 2a - 3a + 6

= a(a - 2) - 3(a - 6)

g(x) = (a - 3)(a - 2)

GCD is (a -2)

f (x) × g(x) = LCM × GCD

LCM = [f(x) × g(x)] / GCD

LCM = [(a + 6)(a - 2) (a - 3)(a - 2)] / a -2

LCM = (a + 6)(a - 2) (a - 3)

Problem 2 :

Find the LCM of the following polynomials whose GCD is (x - 3a).

(x 4 -27a3x) and (x -3a)2

Solution :

Let f(x) = x 4 -27a3x, g(x) = (x -3a)2

f(x) = x(x3 - 27a3)

f(x) = x(x3-(3a)3)

f(x) = x(x-3a)(x2-x(3a)+(3a)2)

f(x) = x (x- 3a)(x2-3ax+9a2)

g(x) = (x -3a)2

GCD is (x -3a)

f (x) × g(x) = LCM × GCD

LCM = [f(x) × g(x)] / GCD

LCM = [x(x- 3a)(x2-3ax+9a2)(x -3a)2] / (x -3a)

LCM = x(x2-3ax+9a2)(x -3a)2