Question

O resto da divisão de
3x⁴-2x³+4x-10 por x-2 é

Answer 1

$\textrm{Pelo Teorema de D'Alembert, teremos:}\\\\ \mathrm{\cfrac{P(x)}{x-a}\ \to\ R(x)=P(a)}\\\\ \textrm{Logo:}\\\\ \mathrm{\cfrac{3x^4-2x^3+4x-10}{x-2}\ \to\ a=2}\\\\ \mathrm{R(x)=P(2)=3.2^4-2.2^3+4.2-10=}\\ \mathrm{=3.16-2.8+8-10=48-16-2=30}\\\\ \mathbf{R(x)=30}$