To determine the least common multiple (LCM) and highest common factor (HCF) of the given expressions x^2 - 2x - 3 and x^2 + 2x - 3, we need to factorize them first:
x^2 - 2x - 3 = (x - 3)(x + 1)
x^2 + 2x - 3 = (x - 1)(x + 3)
Now, we can determine the LCM by taking the product of the highest powers of all the factors:
LCM = (x - 3)(x + 1)(x - 1)(x + 3)
To determine the HCF, we find the common factors with the lowest power:
HCF = (x - 3)(x + 1)
Therefore, the LCM of x^2 - 2x - 3 and x^2 + 2x - 3 is (x - 3)(x + 1)(x - 1)(x + 3), and the HCF is (x - 3)(x + 1).