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25- Sendo P(x) = 2x4 – x3 + x2 + x + 3 e Q(x) = x3 + 2x2 – x + 3, calcule:

 

a) P(x) + Q(x)

b) P(x) – Q(x)

c) Q(x) – P(x)

Resposta :

a)

 

Temos que:

 

[tex]\text{P}(\text{x})=2\text{x}^4-\text{x}^3+\text{x}^2+\text{x}+3[/tex]

 

[tex]\text{Q}(\text{x})=\text{x}^3+2\text{x}^2-\text{x}+3[/tex]

 

Desta maneira, podemos afirmar que:

 

[tex]\text{P}(\text{x})+\text{Q}(\text{x})=(2\text{x}^4-\text{x}^3+\text{x}^2+\text{x}+3)+(\text{x}^3+2\text{x}^2-\text{x}+3)[/tex]

 

[tex]\text{P}(\text{x})+\text{Q}(\text{x})=2\text{x}^4+3\text{x}^2+6[/tex]

 

 

b)

 

[tex]\text{P}(\text{x})-\text{Q}(\text{x})=(2\text{x}^4-\text{x}^3+\text{x}^2+\text{x}+3)-(\text{x}^3+2\text{x}^2-\text{x}+3)[/tex]

 

[tex]\text{P}(\text{x})-\text{Q}(\text{x})=2\text{x}^4-\text{x}^2+2\text{x}[/tex]

 

 

c)

 

[tex]\text{Q}(\text{x})-\text{P}(\text{x})=(\text{x}^3+2\text{x}^2-\text{x}+3)-(2\text{x}^4-\text{x}^3+\text{x}^2+\text{x}+3)[/tex]

 

[tex]\text{Q}(\text{x})-\text{P}(\text{x})=-2\text{x}^4+2\text{x}^3+\text{x}^2-2\text{x}[/tex]

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