Answer:
x - 1 and x + 2
Explanation:
By the factor theorem if (x - a) is a factor then f(a) = 0.
Try x - 1:_
f(1) = 5(1)^3 + 8(1)^2 - 7 - 6
= 5 + 8 - 7 - 7
= 0 so x - 1 is a factor
We can find the other factors by long division:-
5x^2 + 13x + 6
-----------------------------------
x - 1 ) 5x^3 + 8x^2 - 7x - 6
5x^3 - 5x^2
--------------------
13x^2 - 7x
13x^2 - 13x
------------------
6x - 6
6x - 6
-----------------
5x^2 + 13x + 6 = (5x + 3)(x + 2)