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.

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.

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-09-10T19:51:15+02:00

The standard form of a polynomial is: [tex]P(x) = ax^n + bx^{n-1} + cx^{n-2} + .... + d[/tex] where the exponent of the variable decrease to 0.

Marcus and Ariel are both correct.

Given that:

[tex]M \to Marcus[/tex]

[tex]A \to Ariel[/tex]

So, we have:

[tex]M = 3x^3 - 4x^2y + y^2 + 2[/tex]

[tex]A = y^2 - 4x^2y + 3x^3 + 2[/tex]

For Marcus polynomial

[tex]M = 3x^3 - 4x^2y + y^2 + 2[/tex]

The variable is x and the degree of the polynomial is 3.

Marcus' representation is correct

For Ariel polynomial

[tex]A = y^2 - 4x^2y + 3x^3 + 2[/tex]

The variable is y and the degree of the polynomial is 2.

Ariel' representation is also correct

Hence, we can conclude that Marcus and Ariel are correct with their representation of polynomial