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. Which student is correct and why?

Answer 1

Here is the sample response:

They are both correct because there is more than one way to write a multivariable polynomial in standard form. Marcus has the exponents on the x variable in descending order from the highest degree to the lowest degree. Ariel has the exponents on the y variable in descending order from the highest degree to the lowest degree.

You can paraphrase your answer and you should be fine.

Good luck!

-RxL

Answer 2

The degree of a polynomial is the highest power of its terms.
The power of a term is the sum of the powers of all the variables in a term.
A polynomial is written starting with the greatest power in standard form.
In the first case, the power of the first term is 3, the power of the second is 3 (2 from x + 1 from y) but the power of x has decreased so it is the second term, and then so on.
In the second case, the power is starting form 2 and then increasing to 3. This is incorrect.
Therefore, Marcus' suggestion is correct.