Q:

Express the polynomial −g + 3g + 2g2 in standard form and then classify it.

Accepted Solution

A:
Standard Form of Polynomials: When each term is written in the [decreasing; greatest to least] order of degree.
__________________________________________________________
Note 1: A degree of a term is the number of it's exponent.
Note 2: A constant number (A number without an exponent) will have the degree of 0. Always.
Note 3: A variable without a visible exponent obtains an exponent of 1. Ex. x = $$x^{1}$$
Note 4: The operation sign before a coefficient/constant indicates if it's positive or negative. No sign: it's positive. Subtraction sign: value is negative. Addition sign: value is negative.
Note: A degree of a polynomial is the number of it's highest exponent.
Note: (Mono)mials are polynomials with only one term. (Bi)nomials are of only two terms. (Tri)nomials are of only three terms. (Poly)nomials are more than 3 terms.
Mono - One
Bi - Two
Tri - Three
Poly - Many
_________________________________________________________
Step 1: Find the degrees of all the terms1: -g translates to $$-1g^{1}$$ This is the first degree.
2: 3g translates to $$3g^{1}$$ This is the first degree.
3: I am supposing you meant $$2g^{2}$$ for ''2g2''. If you did (most likely), you should do ^ to indicate if the number after that sign is an exponent while the number in front is the base. say for instance, x^2. This translates to $$x^{2}$$ where x is the base and 2 is the exponent. This is the second degree.

Step 2: Order them greatest to least. $$2g^{2}$$ comes first since it's the greatest degree. I'm putting 3g second even if 3g and -g shares the same degree because the number before the variable is greater than -g's number before the variable.

$$2g^{2}$$ + 3g -g
__________________________________________________________
Classifying Polynomials: You can classify polynomials by degree and by the number of terms. First is the degree then then the type of polynomial.

In this case it's 2nd degree trinominal because the highest exponent in a term is 2 and there are three terms within this expression
__________________________________________________________
Answer: $$2g^{2}$$ + 3g -g; 2nd degree trinominal