Correct Question:
Which term could be put in the blank to create a fully simplified polynomial written in standard form?
[tex]8x^3y^2 -\ [\ \ ] + 3xy^2 - 4y3[/tex]
Options
[tex]x^2y^2[/tex] [tex]x^3y^3[/tex] [tex]7xy^2[/tex] [tex]7x^0y^3[/tex]
Answer:
[tex]x^2y^2[/tex]
Step-by-step explanation:
Given
[tex]8x^3y^2 -\ [\ \ ] + 3xy^2 - 4y^3[/tex]
Required
Fill in the missing gap
We have that:
[tex]8x^3y^2 -\ [\ \ ] + 3xy^2 - 4y^3[/tex]
From the polynomial, we can see that the power of x starts from 3 and stops at 0 while the power of y is constant.
Hence, the variable of the polynomial is x
This implies that the power of x decreases by 1 in each term.
The missing gap has to its left, a term with x to the power of 3 and to its right, a term with x to the power of 1.
This implies that the blank will be filled with a term that has its power of x to be 2
From the list of given options, only [tex]x^2y^2[/tex] can be used to complete the polynomial.
Hence, the complete polynomial is:
[tex]8x^3y^2 -x^2y^2+ 3xy^2 - 4y3[/tex]
