Find the remainder when f of x is divided by x - k and ƒ of x equals 2x3 plus 3x2 plus 4x plus 18 and k equals -2?

Find the remainder when f(x) is divided by (x - k)

ƒ(x) = 2x3 + 3x2 + 4x + 18; k = -2

(x - k)

= (x - (-2))

= (x + 2)

x + 2 = 0

x = -2

By Remainder Theorem

ƒ(x) = 2x3 + 3x2 + 4x + 18

ƒ(-2) = 2(-2)3 + 3(-2)2 +4(-2) + 18

= 2(-8) + 3(4) + 4(-2) +18

= -16 + 12 -8 +18

= 6

Thus, the remainder is 6