Final answer:
To factor completely -p⁴-8p³-p²-8p, factor out -p and then factor the remaining expression.
Step-by-step explanation:
To factor completely -p⁴-8p³-p²-8p, we first look for common factors among the terms. In this case, the common factor is -p. Factoring out -p gives us:
-p(p³+8p²+p+8)
The remaining expression, p³+8p²+p+8, can also be factored. Notice that each term has a power of p, so we can factor p out. Factoring out p gives us:
-p(p+2)(p²+4).
Therefore, the complete factored form is -p(p+2)(p²+4).