Question

Which binomial expressions are factors of 2x^3+5x^2-x-6?

Answer 1

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

Answer 2

The answer is x+2 and x-1