Find the remainder using remainder theorem, when

5x³ + 2x² – 6x + 12 is divided by x + 2

5x³ + 2x² – 6x + 12 is divided by x + 2

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) = 5x³ + 2x² – 6x + 12 and we have (x + 2)

The zero of (x + 2) is – 2

Now using Remainder theorem,

p(x) = 5x³ + 2x² – 6x + 12 is divided by x + 2 then, p(–2) is the remainder

p(–2) = 5(–2)³ + 2(–2)² – 6(–2) + 12

= 5×(–8) + 2×4 – (– 12) + 12

= – 40 + 8 + 12 + 12

= – 40 + 32

= – 8

Remainder = –8