Question

Find the Highest Common Factors by Factorization method of (x^2 - 4), (x^3 + 8), and (x + 2)^2.

a) (x + 2)
b) (x - 2)
c) (x + 4)
d) (x - 4)

Answer 1

The Highest Common Factor of the expressions (x^2 - 4), (x^3 + 8), and (x + 2)^2 by factorization is (x + 2).

Step-by-step explanation:

To find the Highest Common Factor (HCF) by factorization method of the given expressions: (x^2 - 4), (x^3 + 8), and (x + 2)^2, we need to factor each expression.

• For (x^2 - 4), this is a difference of squares and can be factored as (x + 2)(x - 2).
• The expression (x^3 + 8) can be factored as a sum of cubes: (x + 2)(x^2 - 2x + 4).
• Finally, (x + 2)^2 is already in factored form.

The common factor in all three expressions is (x + 2). Hence, the HCF is (x + 2).