Question

What is the completely factored form of p⁴−16? Which of the following options represents the correct factorization?

A. (p−2)(p+2)(p²+4)
B. (p−2)(p+2)(−p²+4)
C. (p+2)(p−2)(p²+4)
D. (p−4)(p+4)

Answer 1

The completely factored form of p⁴−16 is (p−2)(p+2)(p²+4).

Step-by-step explanation:

To factor the expression p⁴−16, we can use the difference of squares formula.

The difference of squares formula states that a²−b² can be factored as (a+b)(a−b). In this case, p⁴ is equivalent to (p²)² and 16 is equivalent to 4². Therefore, we can rewrite the expression as (p²)²−4².

Applying the difference of squares formula, we get ((p²)+4)((p²)−4).

Simplifying further, we have (p+2)(p−2)(p²+4). Therefore, the correct factorization of p⁴−16 is option A. (p−2)(p+2)(p²+4).