Find the remainder using remainder theorem, when

8x⁴ + 12x³ – 2x² – 18x + 14 is divided by x + 1

8x⁴ + 12x³ – 2x² – 18x + 14 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) = 8x⁴ + 12x³ – 2x² – 18x + 14 and we have (x + 1)

The zero of (x + 1) is – 1

Now using Remainder theorem,

p(x) = 8x⁴ + 12x³ – 2x² – 18x + 14 is divided by x + 1 then, p(– 1) is the remainder

p(– 1) = 8(–1)⁴ + 12(–1)³ – 2(–1)² – 18(–1) + 14

= 8 – 12 – 2 +18 + 14

= 26

Remainder = 26