Answer:
I think it's 3/10
Step-by-step explanation:
Answer:

Step-by-step explanation:
Since we're dividing the polynomial by
, we'll be using -1 to start the division.
Before setting the division up, let's list the coefficients of
from descending powers and the constant.
The coefficient of
is 3
Since we don't see an
, the coefficient will be 0.
The coefficient of
is 5.
Lastly, the constant, which is the term without the
is -1.
Refer to the attached picture before continuing.
After referring to the picture, we now have the coefficients for the quotient.
The coefficient of
is 3.
The coefficient of
is -3.
The constant is 8.
Lastly, since the last number is not zero, it's the remainder just like regular division. This can be tricky to remember, but -9 is not the actual remainder.
The remainder is actually
.
Now putting all the pieces together, we get:

Answer:
The solution of the given initial value problems in explicit form is
and the solutions are defined for all real numbers.
Step-by-step explanation:
The given differential equation is

It can be written as

Use variable separable method to solve this differential equation.

Integrate both the sides.

![[\because \int x^n=\frac{x^{n+1}}{n+1}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20x%5En%3D%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%5D)
... (1)
It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.



The value of C is -2. Substitute C=-2 in equation (1).
Therefore the solution of the given initial value problems in explicit form is
.
The solution is quadratic function, so it is defined for all real values.
Therefore the solutions are defined for all real numbers.
It has line symmetry and rotational symmetry, so A is the answer, hope this helps