Question

Find the HCF of x - x and x² + x + 1.​

Answer 1

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).

Step-by-step explanation: