Question

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.

Answer 1

I know that 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
marcus is right

Answer 2

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 following order: $3x^3; -4x^2y$);

2. Write the terms with lower exponents in descending order (term $y^2$);

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).

Then the standard form is $3x^3-4x^2y + y^2 + 2$.