Resposta :
[tex]\text{a) }[P(x)]^2 =(x^3+2x^2)^2=(x^3)^2+2.x^3.2x^2+(2x^2)^2= [/tex]
[tex]=x^{3.2}+4x^{3+2}+4x^{2.2}=x^6+4x^5+4x^4=x^4(x^2+4x+4)=[/tex]
=[tex]=x^4(x+2)^2[/tex]
[tex]\text{b) }P(x).Q(x) = (x^3+2x^2)(x^4-x^3+2x-1)=[/tex]
[tex]=x^7-x^6+2x^4-x^3+2x^6-2x^5+4x^3-2x^2=[/tex]
[tex]=x^7+x^6-2x^5+2x^4+3x^3-2x^2[/tex]
[tex]\text{P}(\text{x})=\text{x}^3+2\text{x}^2[/tex]
a)
[tex][\text{P}(\text{x})]^2=(\text{x}^3+2\text{x}^2)^2=(\text{x}^3)^2+2\cdot\text{x}^3\cdot2\text{x}^2+(2\text{x}^2)^2=\text{x}^6+4\text{x}^5+4\text{x}^4[/tex]
[tex][\text{P}(\text{x})]^2=\text{x}^4\cdot(\text{x}^2+4\text{x}+4)=\text{x}^4\cdot(\text{x}+2)^2[/tex]
[tex]\text{Q}(\text{x})=\text{x}^4-\text{x}^3+2\text{x}-1[/tex]
b)
[tex]\text{P}(\text{x})\cdot\text{Q}(\text{x})=(\text{x}^3+2\text{x}^2)\cdot(\text{x}^4-\text{x}^3+2\text{x}-1)[/tex]
[tex]\text{P}(\text{x})\cdot\text{Q}(\text{x})=\text{x}^7-\text{x}^6+2\text{x}^4-\text{x}^3+2\text{x}^6-2\text{x}^5+4\text{x}^3-2\text{x}^2[/tex]
[tex]\text{P}(\text{x})\cdot\text{Q}(\text{x})=\text{x}^7+\text{x}^6-2\text{x}^5+2\text{x}^4+3\text{x}^3-2\text{x}^2[/tex]
[tex]\text{P}(\text{x})\cdot\text{Q}(\text{x})=\text{x}^2\cdot(\text{x}^5+\text{x}^4-2\text{x}^3+2\text{x}^5+3\text{x}-2)[/tex]