Question

find the HCF and LCM f (x)=24(x^3+9x^2+20x) g(x)= 28(x^4+x^3-12x^2)​

Answer 1

Step-by-step explanation:

Answer

We know that HCF is the highest common factor.

Factorise x

3

+x

2

−x−1 as follows:

x

3

+x

2

−x−1=x

2

(x+1)−1(x+1)=(x

2

−1)(x+1)=(x−1)(x+1)(x+1)=(x−1)(x+1)

2

(using identity a

2

−b

2

=(a+b)(a−b))

Now, factorise x

3

+x

2

+x+1 as follows:

x

3

+x

2

+x+1=x

2

(x+1)+1(x+1)=(x

2

+1)(x+1)

Since the common factor between the polynomials x

3

+x

2

−x−1 and x

3

+x

2

+x+1 is (x+1).

Hence, the HCF is (x+1).