Alina fully simplifies this polynomial and then writes it in standard form.

xy2 – 2x2y + 3y3 – 6x2y + 4xy2
if alina wrote the last term as 3y3, which must be the first term of her polynomial in standard form?

a. xy^2
b. 5xy^2
c. –8x^2y
d. –2x^2y

 The correct option is (c).

Step-by-step explanation:  Given that Alina fully simplifies the following polynomial and then writes it in standard form.

We are to find the first term of her polynomial in standard form, if she wrote the last term as

We know that if all the terms of a POLYNOMIAL in two variables x and y has same degree, then in the standard form, it can be written in the descending power of x and ascending power of y,

or, ascending powers of x and descending powers of y.

Since all the terms in Alina's polynomial has degree 3, and the last term is [/tex]3y^3,[/tex] which contains the highest power of y.

So, the polynomial has ascending powers of y, and consequently, it will have descending powers of x.

So, the polynomial in standard form will be

Therefore, the first term in Alina's polynomial is

Option (c) is correct.

Consider polynomial It consists of five terms and

You can group first and last terms: and second and fourth terms: Then

Thus, standard form of polynomial is

(here degrees at x are decreasing and degrees at y are increasing).

, correct choice is C.

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step-by-step explanation: