Question

Find the HCF of the following polynomials.
P(x) = $(x^4-81)$
Q(x) = $(x^3-27)$

• A. $(x-3)$
• B. $(x^2-9)$
• C. $(x+3)$
• D. $(x^2+9)$

Answer 1

The correct option is A $(x-3)$

P(x) = $(x^4-81)=(x^2-9)(x^2+9)=(x-3)(x+3)(x^2+9)$
Q(x) =$(x^3-27)=(x-3)(x^2+3x+9)$

The common irreducible factors of P(x) and Q(x) is (x-3)
The smallest exponent of the factor common in P(x) and Q(x) is 1.

Hence, the HCF = $(x-3)$.