If HCF of (p2 - 8p + 12) and (p2 + 4p - 12) is (p - a), then the value of a is:

The highest common factor (HCF) of two polynomials is the largest-degree expression that divides both of them exactly. To find it, factorize each polynomial into simpler factors — any factor common to both factorizations is a factor of their HCF, and if exactly one factor is shared, that factor itself is the HCF.

1. Factorize p2 - 8p + 12: find two numbers that multiply to 12 and add to -8, namely -6 and -2, so p2 - 8p + 12 = (p - 6)(p - 2).

2. Factorize p2 + 4p - 12: find two numbers that multiply to -12 and add to 4, namely 6 and -2, so p2 + 4p - 12 = (p + 6)(p - 2).

3. Compare the two factorizations: (p - 6)(p - 2) and (p + 6)(p - 2). The only factor common to both is (p - 2).

4. Since the HCF is given as (p - a), equating p - a = p - 2 gives a = 2.

Substituting p = 2 into both original polynomials confirms it is a root of each: p2 - 8p + 12 = 4 - 16 + 12 = 0, and p2 + 4p - 12 = 4 + 8 - 12 = 0. This independently verifies that (p - 2) is a common factor, so a = 2.