Question

find the remainder when the polynomial 3x^2-x^3+4 is divided by (x+1)​

Answer 1

Answer:

$let \: p(x) = 3x {}^{2} - x {}^{3} + 4 \\ and \: g(x) = x \ + 1 \\ \: \: \: \: \: \: \: \: x = - 1$

By the remainder theorem, we know that p(x) is divided by (x+1) then the remainder is p(-1).

$= p(x) = 3(x) {}^{2} - x + 4 \\ =(p - 1) = 3x( - 1) {}^{2} - ( - 1) {}^{3} + 4 \\ = 3 \times 1 - ( - 1) + 4 \\ =3 + 1 + 4 \\ = 8$