When p (x) = (x 3 + ax 2 + 2x + a) is divided by (x + a), the remainder is

Question

Philoid · Accepted Answer

We have,

(x³ + ax² + 2x + a)

Let, p (x) = (x³ + ax² + 2x + a)

And, x + a = 0

x = - a

It is given that, (x + a) is a factor of p (x) so the remainder is equal to p (-a)

∴ p (-a) = (-a)³ + a (-a)² + 2 (-a) + a

= - a³ + a³ – 2a + a

= - a

Hence, option C is correct