Question

Obter o quociente e o resto da divisao de f(x)= -3x³ +2x² +4 por g (x)=x+1

Answer 1

$f(x)=-3x^{3}+2x^{2}+4\\ \\ =-3x^{3}-3x^{2}+3x^{2}+2x^{2}+4\\ \\ =-3x^{2}\left(x+1 \right )+5x^{2}+4\\ \\ =-3x^{2}\left(x+1 \right )+5x^{2}+5x-5x+4\\ \\ =-3x^{2}\left(x+1 \right )+5x\left(x+1 \right )-5x+4\\ \\ =-3x^{2}\left(x+1 \right )+5x\left(x+1 \right )-5x-5+5+4\\ \\ =-3x^{2}\left(x+1 \right )+5x\left(x+1 \right )-5\left(x+1 \right )+5+4\\ \\ =-3x^{2}\left(x+1 \right )+5x\left(x+1 \right )-5\left(x+1 \right )+9\\ \\ =\left(x+1 \right )\underbrace{\left(-3x^{2}+5x-5 \right )}_{\text{quociente}}+\underbrace{9}_{\text{resto}}$