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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.

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apologiabiology

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

frika

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 \(3x^3-4x^2y + y^2 + 2\).

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