Question

Which algebraic expression is a polynomial? Which term could be put in the blank to create a fully simplified polynomial written in standard form? 8x3y2−_____+3xy2−4y3 x2y2 x3y 7xy2 7x0y3

Answer 1

Answer:

$x^3y$ and  $x^2y^2$

Step-by-step explanation:

An algebraic expression is a polynomial if and only if the variables involve have positive integral indices or exponents.

The given polynomial is: $8x^3y^2----------+3xy^2$

We want to put one of the following polynomials in the blank space to create a fully simplified polynomial written in standard form.

$-4y^3$

$x^2y^2$

$x^3y$

$7x^2y$

$7x^0y^3$

A fully simplified polynomial written in standard form is obtained by writing the simplified polynomial in decreasing order according to degree.

Since the first term of  $8x^3y^2----------+3xy^2$ having a degree of 5 and the last term is having a degree of 3.

The polynomial that goes into the blank must have a degree of 4.

This eliminates $-4y^3$, $7x^2y$

and $7x^0y^3$

We are now left with $x^2y^2$ and $x^3y$

The required polynomial is therefore $8x^3y^2-x^2y^2+3xy^2$ or$8x^3y^2-x^3y+3xy^2$

These two polynomials are in standard form and cannot be simplified further.

The correct choices are;

$x^3y$ and  $x^2y^2$

Answer 2

Answer:x2y2

Step-by-step explanation: