Respuesta :
The completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.
What is polynomial?
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).
The polynomial equation given in the problem is,
[tex]p^4 - 16[/tex]
Let the factor form of the polynomial is f(p). Thus,
[tex]f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2[/tex]
Using the formula of difference of squares, we get,
[tex]f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)[/tex]
Thus, the completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.
Learn more about polynomial here;
https://brainly.com/question/24380382
