The HCF of the polynomials  is:

The correct answer is: the HCF is(x + 4)(x - 1).

Step 1 of 2:
Simplify both the expressions,

= x (x - 1) - 1(x - 1)(x + 4)
                                           = (x - 1)(x - 1)(x + 4)

Similarly,
= x (x + 4) - 1(x + 4)(x + 1)
                                          = (x - 1)(x + 4)(x + 1)
Step 2 of 2:
Analyze the factors of the expressions;


Now, find the highest common factors in these expressions .Thus, we have:
(x + 4)(x - 1)
Hence, the HCF is(x + 4)(x - 1).

HCF of any of two numbers is their highest value that divides them both simultaneously.