Question

When p(x) = x³ + ax² + 2x + a is divided by (x+a),the remainder is ?
(how to solve it without dividing)​

Answer 1

Answer:

$p(x) = {x}^{3} + a {x}^{2} + 2x + a \\ let \: g(x) = ( x + a) \\ (x + a) = 0 \\ x = - a \\ \\ put \: the \: value \: of \: x \: in \: p(x) \\ p( - a) = {a}^{3} + a \times {a}^{2} + 2 \times a + a \\ = {a}^{3} + {a}^{3} + 2a + a \\ = 2{a}^{3} + 3a$