Q1. How do I know what a expression is called for example 6x^3-9x+3?

it is a polynomial because it is a sum of terms which are coefficients times x^n where n can be any old whole numbers

Since the highest n in this expression is three it is called a cubic polynomial

Thanks-got it cubic trinomial. Here's another one when I have to change signs of negatives and positives for addition and subtraction. How do I do for example 5w^2-4w-7-8w^2+3w-3?

If you just want the name that is a quadratic polynomial because the highest power of w is 2.

your alternating signs make no difference at all. Like 5 w^2 - 8 w^2 = -3w^2

No I do not want the Name I want to know how to figure it out once the numbers are all lined up and it is very confusing when signs need to be switched. Can you please explain that?

5 w^2 - 8 w^2 = -3 w^2

-4 w + 3 w = -1 w

-3 = -3

so
-3 w^2 - 1 w - 3
or
- (w^2 + w +3)

Thanks. There was ( ) on the 8 and the rest because your answer is not one of the answers

To know what a mathematical expression is called, such as 6x^3 - 9x + 3, you need to understand the terms used to classify expressions. In this case, the expression you provided is called a polynomial. Here's how to identify and classify it:

1. Identify the variables: In this expression, the variable is "x." Variables are the placeholders for unknown values or quantities.

2. Identify the coefficients: Coefficients are the numbers that multiply the variables. In this case, the coefficients are 6, -9, and 3.

3. Identify the exponents: Exponents are the superscripts that indicate the power or degree to which the variables are raised. In this expression, "x^3" means that x is raised to the power of 3. If there are no exponents explicitly mentioned, it is assumed to be 1.

4. Identify the operators: The operators in this expression are addition (+) and subtraction (-). These operators determine the combination of terms within the expression.

By considering these aspects, we can classify the expression as a polynomial. Polynomials are expressions consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. Specifically, your expression is a third-degree polynomial because the highest exponent is 3.

Remember, the ability to identify and name expressions develops with familiarity and practice, so keep exploring and studying different types of expressions to enhance your understanding.