Question

Do the problem 1) find the L.C.M of the polynomial 12(x^4-x^3) and (x^4-3x^3+2x^2). 2) if (x-k) is the H.C.F of x^2+x-12 and 2x-^2kx-9,then 'k'= a) 2 b) 3 c) 4 d) -2​

Answer 1

Step-by-step explanation:

Factorise all the polynomials

3x2−6x=3x(x−2) 

x2−4x+4=(x−2)(x−2)

x2+x−6=(x−2)(x+3)

The least common multiple for the first two polynomials is 3x(x−2)2

The LCM of three polynomials is LCM of 3x(x−2)2 and (x−2)(x−3)

⇒LCM=3x(x−22)(x+3)

The highest common factor of first two polynomials is (x−2)

The HCF of all the three polynomials is HCF of (x−2) and (x−2)(x−3)

⇒HCF=(x−2)