Question

which represents the polynomial written in standard form?
$8x^2y^2 - 3x^3y + 4x^4 - 7xy^3$
$\bigcirc\\ 4x^4 - 3x^3y + 8x^2y^2 - 7xy^3$
$\bigcirc\\ 4x^4 - 7xy^3 - 3x^3y + 8x^2y^2$
$\bigcirc\\ 4x^4 + 8x^2y^2 - 3x^3y - 7xy^3$
$\bigcirc\\ -7xy^3 - 3x^3y + 8x^2y^2 + 4x^4$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in two variables (x and y here) is in standard form when terms are ordered by decreasing degree of \(x\) (or by decreasing sum of exponents of \(x\) and \(y\), but here we can use degree of \(x\)). The degree of a term \(ax^m y^n\) in \(x\) is \(m\).

Step2: Find degree of each term

• For \(8x^{2}y^{2}\): degree of \(x\) is \(2\)
• For \(-3x^{3}y\): degree of \(x\) is \(3\)
• For \(4x^{4}\): degree of \(x\) is \(4\)
• For \(-7xy^{3}\): degree of \(x\) is \(1\)

Step3: Order terms by decreasing degree of \(x\)

Order from highest degree of \(x\) to lowest:

• \(4x^{4}\) (degree 4)
• \(-3x^{3}y\) (degree 3)
• \(8x^{2}y^{2}\) (degree 2)
• \(-7xy^{3}\) (degree 1)

So the polynomial in standard form is \(4x^{4}- 3x^{3}y + 8x^{2}y^{2}-7xy^{3}\)

Answer:

A. \(4x^{4}- 3x^{3}y + 8x^{2}y^{2}-7xy^{3}\)