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:
