Answer:
![p(x) = {x}^{3} + 4{x}^{2} + 22x- 68](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20%2B%204%7Bx%7D%5E%7B2%7D%20%20%2B%2022x-%2068)
Step-by-step explanation:
We want to write an equation for the polynomial function with roots;
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
and
![x = - 3 + 5i](https://tex.z-dn.net/?f=x%20%3D%20%20-%203%20%2B%205i)
Note that complex roots come in pairs and in conjugates.
Therefore
![x = - 3 - 5i](https://tex.z-dn.net/?f=x%20%3D%20%20-%203%20-%205i)
is also a root.
By the factor theorem:
(x-2), (x+3+5i), and (x+3-5i) are factors of the polynomial.
Let p(x) be the polynomial, then in factored form.
![p(x) = (x - 2)(x + 3 + 5i)(x + 3 - 5i)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%20-%202%29%28x%20%2B%203%20%2B%205i%29%28x%20%2B%203%20-%205i%29)
We expand now to get:
![p(x) = (x - 2)( {x}^{2} + 3x - 5ix + 3x + 9 - 15i + 5ix + 15i + 25)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%20-%202%29%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%203x%20%20-%20%205ix%20%2B%203x%20%2B%209%20-%2015i%20%2B%205ix%20%2B%2015i%20%2B%2025%29)
Simplify now
![p(x) = (x - 2)( {x}^{2} + 6x +34)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%20-%202%29%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B34%29)
We expand further;
![p(x) = x( {x}^{2} + 6x + 34) - 2( {x}^{2} + 6x + 34)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20x%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%2034%29%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%2034%29)
![p(x) = {x}^{3} + 6 {x}^{2} + 34x - 2 {x}^{2} - 12x - 68](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20%2B%206%20%7Bx%7D%5E%7B2%7D%20%20%2B%2034x%20-%202%20%7Bx%7D%5E%7B2%7D%20%20%20-%2012x%20%20-%2068)
![p(x) = {x}^{3} + 4{x}^{2} + 22x- 68](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20%2B%204%7Bx%7D%5E%7B2%7D%20%20%2B%2022x-%2068)
¢30 every day because 10divided by 3 is .3
Answer:
sorry i cant help
Step-by-step explanation:
Answer:
its 23
Step-by-step explanation:
its 12+11 because two negatives make a positive
It’s 1/8 I don’t feel like explaining it but trust me