To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.
The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15
x² - y² is common in both polynomials, let's factor it out.
x² - y² = (x-y)(x+y)
so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3
and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15
So the HCF of these two polynomials is (x-y)(x+y)
It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.