The completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.
<h3>What is polynomial?</h3>
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,
![p^4 - 16](https://tex.z-dn.net/?f=p%5E4%20-%2016)
Let the factor form of the polynomial is f(p). Thus,
![f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2](https://tex.z-dn.net/?f=f%28p%29%3Dp%5E4%20-%2016%5C%5Cf%28p%29%3Dp%5E4%20-%202%5E4%5C%5Cf%28p%29%3D%28p%5E2%29%5E2-%20%282%5E2%29%5E2)
Using the formula of difference of squares, we get,
![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)](https://tex.z-dn.net/?f=f%28p%29%3D%28p%5E2-4%29%28p%5E2%2B4%29%5C%5Cf%28p%29%3D%28p%5E2-2%5E2%29%28p%5E2%2B4%29%5C%5Cf%28p%29%3D%28p-2%29%28p%2B2%29%28p%5E2%2B4%29)
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;
brainly.com/question/24380382
For this case we must simplify the following expression:
![x ^ 2-3xy-5xy-7y ^ 2 + 4x ^ 2 + 8y ^ 2](https://tex.z-dn.net/?f=x%20%5E%202-3xy-5xy-7y%20%5E%202%20%2B%204x%20%5E%202%20%2B%208y%20%5E%202)
We must add similar terms taking into account that:
- Equal signs are added and the same sign is placed.
- Different signs are subtracted and the major sign is placed.
![(x ^ 2 + 4x ^ 2) + (- 3xy-5xy) + (- 7y ^ 2 + 8y ^ 2) =\\5x ^ 2-8xy + y ^ 2](https://tex.z-dn.net/?f=%28x%20%5E%202%20%2B%204x%20%5E%202%29%20%2B%20%28-%203xy-5xy%29%20%2B%20%28-%207y%20%5E%202%20%2B%208y%20%5E%202%29%20%3D%5C%5C5x%20%5E%202-8xy%20%2B%20y%20%5E%202)
Thus, the simplified expression is:
![5x ^ 2-8xy + y ^ 2](https://tex.z-dn.net/?f=5x%20%5E%202-8xy%20%2B%20y%20%5E%202)
Answer:
![5x ^ 2-8xy + y ^ 2](https://tex.z-dn.net/?f=5x%20%5E%202-8xy%20%2B%20y%20%5E%202)
Answer:
x=y^2-2
Step-by-step explanation:
This graph, is a parabola that opens to the right.
To answer this question, we just use the vertex form of a sideways parabola- x=a(y-k)^2+h.
In this case, the vertex is (-2, 0), and our value of a is 1, since it opens to the right.
This gives us: x=1(y-0)^2+(-2)
Which simplifies to: x=y^2-2.
Also, the answer to the previous two questions are wrong.
The D value (Domain) is actually [2, ∞)
The R value (Range) is actually "All real numbers" (-∞, ∞)
Let me know if this helps!
Answer:
There are 2
(6 2/5, -6 2/5)
(8 3/5, 4 2/5)
Step-by-step explanation: