Find the remainde

x³ – ax² – 5x + 2a is divided by x – a

Remainder theorem states that if p(x) is any polynomial and a is any real number and If p(x) is divided by the linear polynomial (x – a) , then the remainder is p(a).

Let p(x) = x³ – ax² – 5x + 2a and we have (x – a)

The zero of (x – a) is a

Now using Remainder theorem,

p(x) = x³ – ax² – 5x + 2a is divided by x – a then, p(a) is the remainder

p(a) = (a)³ – a(a)² – 5(a) + 2a

= a³ – a³ – 5a+ 2a

= – 3a

Remainder = –3a