Find the remainder using remainder theorem, when

3x³ + 4x² – 5x + 8 is divided by x – 1

3x³ + 4x² – 5x + 8 is divided by x – 1

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) = 3x³ + 4x² – 5x + 8 and we have (x – 1)

The zero of (x – 1) is 1

Now using Remainder theorem,

p(x) = 3x³ + 4x² – 5x + 8 is divided by x – 1 then, p(1) is the remainder

p(1) = 3(1)³ + 4(1)² – 5(1) + 8

= 3 + 4 – 5 + 8

= 10

Remainder = 10