Question

(x^3 + 8x^2 + kx + 4) ÷ (x+ 2)

Please help how do i solve for k please include steps this is called remainder theorem

Answer 1

k = 14

Explanation:

The Remainder theorem states that if f(x) is divided by (x + h) then the remainder is f(- h)

If (x + h) is a factor of f(x) then the remainder is zero, that is f(- h) = 0

Given (x + 2) is a factor of f(x) then f(- 2) = 0, that is

(- 2)³ + 8(- 2)² - 2k + 4 = 0

- 8 + 8(4) - 2k + 4 = 0

- 8 + 32 - 2k + 4 = 0

- 2k + 28 = 0 ( subtract 28 from both sides )

- 2k = - 28 ( divide both sides by - 2 )

k = 14

Answer 2

Answer: 14

Explanation:

Check it