Question

PLEASE EXPLAIN THIS PLZ HELP THX:)

Answer 1

Binomial
Bi means two. So you have 2 terms in a binomial. x^2 + 2 is a binomial. In this example, they cannot be added.  There is one sign between the 2 terms. In this case a plus sign.
You have a binomial in the question's table. It is 3x - 9. 2 terms 1 sign.

Trinomial
Tri means three. You have 3 terms in a trinomial. You normally have 2 signs (at least) but you could have 3. All the terms are unlike.
x^2 + 2x - 1 is a a trinomial.
You have 1 trinomial in your question. 
y = - 3x^2 - 6x + 9 
This has 3 signs which is not normal but it is not unique.

Monomial
Mono means one. You have two monomials in your question.
2x^2 and - 2 Yes a constant can be a monomial.

Quadratic.
A quadratic has very specific properties.
The highest power of a quadratic must be x^2.
x^2 + 3x + 2 is a quadratic.
3x^2 - 4x + 2 is a quadratic.
-2x^2 - 5x + 3 is a quadratic.
x^2 + 5 is a quadratic.
- 2x^2 is a quadratic.

A quadratic may or may not have a linear term as in 3x
A quadratic may or may not have a constant term [yet to be defined]

Linear 
A linear equation must have 1 on the variable on both sides of the equal sign.
y = 3x is linear
y = 3x + 7 is linear.
y + 3 = 3x + 2 is linear. The 3 can be put on the right by subtracting 3 from both sides.
y = 2x - 1
y= 3x - 9 is a linear equation.
When you graph 3x - 9 you get a straight line.
y = 3x - 9, you get a straight line. Go to desmos and try it.

Constant.
Has no variables associated connected to it although a line can consist of a constant on one side.
3 is a constant. 
34 is a constant.
y = 8 is constant. It is a line that is parallel to the x axis going through 8.
0 is a constant.
y = 0 is the x axis.

Exponential
is a constant raised to a variable power.
y = 3^x. You don't have one of these.

Naming by power.
You have two equations that are raised to the power of 2.
One is the first monomial
the second is the last one.

One has a power going to 1 ( the third one)

What's the power on the constant.

Answer 2

                                          2d column  number terms    1st name using degree   
2x² - no sighs + or - so it is      monomial                            x² ---quadratic
that divides like(a+b),or (a-b)
only multiplication

-2 -no sighs + or - so it is           monomial                               no x, constant
3x - 9 "-" divides 2 monomials    binomial                              x,    linear
-x²- 3x + 9                                    trinomial                             x²,so quadratic