Marcus states that the polynomial expression 3x3 - 4x2y + y2 + 2 is in standard form. Ariel states that it should be y2 - 4x2y + 3x3 + 2. Explain which student is correct and why.

Here Ariel is wrong because 3x^3 is higher power than y^2

3x^3 goes first

then the mixed term - 4x^2y

then the y^2

then the 2

So, Marcus is right

Standard form means that you write the terms by descending degree. here's main rules how to write polynomial expression in the standard form:

1. write the term with the highest exponent first (terms of third degree in our case 3x^3);

2. write the terms with lower exponents in descending order (term - 4x^2y followed by y^2);

3. remember that a variable with no exponent has an understood exponent of 1 (here are no such terms);

4. a constant term (a number with no variable) always goes last (term 2).