Find the remainder using remainder theorem, when

4x³ – 3x² + 2x – 4 is divided by x + 3

4x³ – 3x² + 2x – 4 is divided by x + 3

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) = 4x³ – 3x² + 2x – 4 and we have (x + 3)

The zero of (x + 3) is – 3

Now using Remainder theorem,

p(x) = 4x³ – 3x² + 2x – 4 is divided by x + 3 then, p(– 3) is the remainder

p(– 3) = 4(–3)³ – 3(–3)² + 2(–3) – 4

= – 108 – 27 – 6 – 4

= – 145

Remainder = –145