given a polynomial with factor (x - a)
Then x = a is a root of the polynomial and f(a) = 0
(1)
(x+ 2) is a factor , hence x = - 2 is a root
Evaluate the polynomial for x = - 2
f(- 2) = 5(- 2)³ + 8(- 2)² - 7(- 2) - 6 = - 40 + 32 + 14 - 6 = 0
Hence (x + 2 ) is a factor
(2)
If (x + 1) is a factor then x = - 1 is a root
5(- 1)³ + 8(-1)² - 7(- 1) - 6 = -5 + 8 + 7 - 6 = 4
Since f( - 1) ≠ 0
Then (x + 1) is not a factor
