x - 2 = 0 , x + 2 = 0 , x + 1 = 0 , x -1 = 0 x = 2 , x = - 2 , x = - 1 , x = 1So we shall check these by putting in 5x^3+8x^2−7x−6 one by one.
Putting x = - 2 , we get 5(-2)^3+8(-2)^2−7(-2)−6= 5 (-8) + 8(4) +14 - 6= -40 + 32 + 8 = 0So x + 2 is a factor of given equation.
Putting x = 2 , we get 5(2)^3+8(2)^2−7(2)−6= 5 (8) + 8(4) -14 - 6= 40 + 32 -20= 52So x - 2 is a not a factor of given equation.
Putting x = - 1 , we get 5(-1)^3+8(-1)^2−7(-1)−6= 5 (-1) + 8(1) +7 - 6= -5 + 8 + 1 = 4So x + 1 is not a factor of given equation.
Putting x = 1 , we get 5(1)^3+8(1)^2−7(1)−6= 5 (1) + 8(1) -7 - 6= 5 + 8 -13 = 0So x -1 is a factor of given equation.
Answer x-1 and x+2
