Answer:
The novel has 117 pages
Step-by-step explanation:
Let p be the pages in the novel
p
−
3
=
114
p
=
117
Given:
A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .
To find:
The fourth-degree polynomial function in factored form.
Solution:
The factor for of nth degree polynomial is:
![P(x)=(x-a_1)(x-a_2)...(x-a_n)](https://tex.z-dn.net/?f=P%28x%29%3D%28x-a_1%29%28x-a_2%29...%28x-a_n%29)
Where,
are n zeros of the polynomial.
It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:
![P(x)=(x-4)(x-(-4))(x-4i)(x-(-4i))](https://tex.z-dn.net/?f=P%28x%29%3D%28x-4%29%28x-%28-4%29%29%28x-4i%29%28x-%28-4i%29%29)
![P(x)=(x-4)(x+4)(x-4i)(x+4i)](https://tex.z-dn.net/?f=P%28x%29%3D%28x-4%29%28x%2B4%29%28x-4i%29%28x%2B4i%29)
![[\because a^2-b^2=(a-b)(a+b)]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%5D)
On further simplification, we get
![P(x)=(x-4)(x+4)(x^2-4^2i^2)](https://tex.z-dn.net/?f=P%28x%29%3D%28x-4%29%28x%2B4%29%28x%5E2-4%5E2i%5E2%29)
![[\because i^2=-1]](https://tex.z-dn.net/?f=%5B%5Cbecause%20i%5E2%3D-1%5D)
Therefore, the required fourth degree polynomial is
.