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What binomial do you have to add to the polynomial:
[tex]2x^{2} +3y^{2} -5xy+1[/tex]
to get the following?
A polynomial that does not contain the variable x
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Same thing but get a polynomial that does not contain the variable y:
[tex]2x^{2} +3y^{2} -5xy+1[/tex]

Respuesta :

semsee45

Answer:

a)  [tex]-2x^2+5xy[/tex]

b)  [tex]-3y^2+5xy[/tex]

Step-by-step explanation:

Part (a)

Given polynomial  :[tex]2x^2+3y^2-5xy+1[/tex]

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

[tex]-2x^2+5xy[/tex]

[tex](2x^2+3y^2-5xy+1)+(-2x^2+5xy)[/tex]

[tex]=2x^2+3y^2-5xy+1-2x^2+5xy[/tex]

[tex]=2x^2-2x^2+3y^2-5xy+5xy+1[/tex]

[tex]=3y^2+1[/tex]

Part (b)

Given polynomial  :[tex]2x^2+3y^2-5xy+1[/tex]

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

[tex]-3y^2+5xy[/tex]

[tex](2x^2+3y^2-5xy+1)+(-3y^2+5xy)[/tex]

[tex]=2x^2+3y^2-5xy+1-3y^2+5xy[/tex]

[tex]=2x^2+3y^2-3y^2-5xy+5xy+1[/tex]

[tex]=2x^2+1[/tex]

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