which not a linear factor of the polynomial x^3-13x-12

Question

x+2

x+3

x-4

x-3

Answer 1

Let x³ - 13x - 12 = 0

 

If (x + 2) is a linear factor, then x = -2 is a solution of the above equation

 

(-2)³ - 13(-2) - 12 = -8 + 26 - 12 = 18 - 12 = 6, so x = -2 is not a solution and (x + 2) is not a linear factor

 

let x = -3, then (-3)³ - 13(-3) - 12 = -27 + 39 - 12 = 12 - 12 = 0, so x = -3 is a solution and (x + 3) is a linear factor

 

let x = 4, then (4)³ - 13(4) - 12 = 64 - 52 - 12 = 12 - 12 = 0, so x = 4 is a solution and (x - 4) is a linear factor

 

let x = 3, then (3)³ - 13(3) - 12 = 27 - 39 - 12 = -12 - 12 = -24, so x = 3 is not a solution and (x - 3) is not a linear factor