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?

Question

Amos

Mathematics

13 December, 11:32

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?

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Answers (1)

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Allison Hurst · Answer 1

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.