Question

one of the factors of 3p^5 - 12p^3 is
p^4
p + 2
p^2 + 4
4

Explanation:

Step1: Factor out the GCF

First, factor out the greatest - common factor of \(3p^{5}-12p^{3}\). The GCF of \(3p^{5}\) and \(12p^{3}\) is \(3p^{3}\). So, \(3p^{5}-12p^{3}=3p^{3}(p^{2} - 4)\).

Step2: Factor the difference of squares

The expression \(p^{2}-4\) is a difference of squares, which can be factored as \((p + 2)(p - 2)\) according to the formula \(a^{2}-b^{2}=(a + b)(a - b)\) where \(a = p\) and \(b = 2\). So, \(3p^{5}-12p^{3}=3p^{3}(p + 2)(p - 2)\).

Answer:

B. \(p + 2\)