When the polynomial 2x³ – 2x² + 9x – 8 is divided by x – 3 the remainder is 28. Find the value of a.

2x³ – ax² + 9x – 8 is divided by x – 3 and remainder = 28

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) = 2x³ – ax² + 9x – 8 and we have (x – 3)

The zero of (x – 3) is 3

Now using Remainder theorem,

p(x) = 2x³ – ax² + 9x – 8 is divided by x – a then, p(3) is the remainder which is 28

p(3) = 2x³ – ax² + 9x – 8 =28

= 2(3)³ – a(3)² + 9(3) – 8 =28

= 54 – 9a + 27 – 8 = 28

= 73 – 9a = 28

= 9a = 73 –28

= 9a = 45

a = 5