Answer: n = - 6
Step-by-step explanation:
Given (x + h) is a factor of a polynomial f(x) then f(- h) = 0
Here
f(x) = x³ + 2x² - 5x + n and (x + 3) is a factor then f(- 3) = 0 , that is
f(- 3) = (- 3)³ + 2(- 3)² - 5(- 3) + n = 0 , so
- 27 + 2(9) + 15 + n = 0
- 27 + 18 + 15 + n = 0
6 + n = 0 ( subtract 6 from both sides )
n = - 6
