Question

What binomial do you have to add to the polynomial:


`2x^(2) +3y^(2) -5xy+1`
to get the following?
A polynomial that does not contain the variable x
--------------
Same thing but get a polynomial that does not contain the variable y:

`2x^(2) +3y^(2) -5xy+1`

Answer 1

a)
`-2x^2+5xy`

b)
`-3y^2+5xy`

Explanation:

Part (a)

Given polynomial :
`2x^2+3y^2-5xy+1`

The binomial that should be added to the given polynomial to get a polynomial that does not contain the variable x is:

`-2x^2+5xy`

`(2x^2+3y^2-5xy+1)+(-2x^2+5xy)`

`=2x^2+3y^2-5xy+1-2x^2+5xy`

`=2x^2-2x^2+3y^2-5xy+5xy+1`

`=3y^2+1`

Part (b)

Given polynomial :
`2x^2+3y^2-5xy+1`

The binomial that should be added to the given polynomial to get a polynomial that does not contain the variable y is:

`-3y^2+5xy`

`(2x^2+3y^2-5xy+1)+(-3y^2+5xy)`

`=2x^2+3y^2-5xy+1-3y^2+5xy`

`=2x^2+3y^2-3y^2-5xy+5xy+1`

`=2x^2+1`