Question

Which binomial expressions are factors of 5x^3+8x^2−7x−6? Select each correct answer. x−2

x + 2

x + 1

x−1

Answer 1

x - 2 = 0 ,    x + 2 = 0  ,   x + 1 = 0 ,  x -1 = 0

  x  = 2 ,      x  =  - 2  ,  x  = - 1    ,   x = 1

So 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 = 0

So 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= 52

So 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 = 4

So 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 = 0

So x -1 is a factor of given equation.