O polinômio x3 + 2x2 – 3x + m ao ser dividido por x + 1, deixa resto 11. Desta forma, qual é o valor da metade de m
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Boa noite PLS!
Solução!
Para resolver esse exercicio tem que lembra do teorema de Alambert.
![P(x)=Resto\\\\\
D(x)=x+1\\\\
x=-1\\\\
Resto=6](https://tex.z-dn.net/?f=P%28x%29%3DResto%5C%5C%5C%5C%5C%0AD%28x%29%3Dx%2B1%5C%5C%5C%5C%0Ax%3D-1%5C%5C%5C%5C%0AResto%3D6 "P(x)=Resto\\\\\
D(x)=x+1\\\\
x=-1\\\\
Resto=6")
![x^{3}+2 x^{2} -3x+m=11\\\\\\
(-1)^{3} +2(-1)^{2}-3(-1)+m=11\\\\\\
-1+2+3+m= 11\\\\\
4+m=11\\\\\
m=11-4\\\\\
m=7](https://tex.z-dn.net/?f=+x%5E%7B3%7D%2B2+x%5E%7B2%7D+-3x%2Bm%3D11%5C%5C%5C%5C%5C%5C%0A%28-1%29%5E%7B3%7D+%2B2%28-1%29%5E%7B2%7D-3%28-1%29%2Bm%3D11%5C%5C%5C%5C%5C%5C%0A-1%2B2%2B3%2Bm%3D+11%5C%5C%5C%5C%5C%0A4%2Bm%3D11%5C%5C%5C%5C%5C%0Am%3D11-4%5C%5C%5C%5C%5C%0Am%3D7+ "x^{3}+2 x^{2} -3x+m=11\\\\\\
(-1)^{3} +2(-1)^{2}-3(-1)+m=11\\\\\\
-1+2+3+m= 11\\\\\
4+m=11\\\\\
m=11-4\\\\\
m=7")
![Metade~~de~~m!\\\\\\
m= \dfrac{7}{2}\\\\\
\boxed{m=3,5}](https://tex.z-dn.net/?f=Metade%7E%7Ede%7E%7Em%21%5C%5C%5C%5C%5C%5C%0Am%3D+%5Cdfrac%7B7%7D%7B2%7D%5C%5C%5C%5C%5C%0A%5Cboxed%7Bm%3D3%2C5%7D+%0A%0A%0A "Metade~~de~~m!\\\\\\
m= \dfrac{7}{2}\\\\\
\boxed{m=3,5}")
Boa noite!
Bons estudos!
Solução!
Para resolver esse exercicio tem que lembra do teorema de Alambert.
Boa noite!
Bons estudos!
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