Question

Find the H.C.F of the following expressions. 1) x²+5x+6 , x²+4x-12. 2) x³-2x²+x , x²+2x-3 , x²+3x-4. don't give irrelevant answer please ​

Answer 1

x^2-3x+2=x^2-2x-x+2

x(x−2)−1(x−2)=(x−2)(x−1)

Now

x ^2 −4x+3=x ^2 −3x−x+3

x(x−3)−1(x−3)=(x−3)(x−1)

Answer 2

Answer:

ANSWER

Factorise all the polynomials

3x

2

−6x=3x(x−2)

x

2

−4x+4=(x−2)(x−2)

x

2

+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−2

2

)(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)