Question

What must be added to the polynomial 2x³ − 3x² − 8x so that it leaves a remainder 10 when divided by (2x + 1)?

Answer 1

Let the number added be k

p(x) = 2x³ − 3x² − 8x + k

Let 2x + 1 = 0

x = `-1/2`

When p(x) is divided by 2x + 1, the remainder is,

p(x) = 10

⇒ `2(-1/2)^3 - 3(-1/2)^2 - 8(-1/2)` + k = 10

⇒ `2(-1/8) - 3(1/4) - 8 (-1/2)` + k = 10

⇒ `-1/4 - 3/4` + 4 + k = 10

⇒ −1 + 4 + k = 10

⇒ 3 + k = 10

⇒ k = 10 − 3

⇒ k = 7