Question

3. When kx³ + x² - 5x -5 is divided by x + 1, its remainder is 0. Hence, the value of k is?​​

Answer 1

k = 1

Explanation:

given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0

here the polynomial is divided by (x + 1)

then substitute x = - 1 into the polynomial and equate to zero

k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0

- k + 1 + 5 - 5 = 0

- k + 1 = 0 ( subtract 1 from both sides )

- k = - 1 ( multiply both sides by - 1 )

k = 1