10. Which is a linear factor of the following expression?
        8x² - 10x - 3
 

 Solution: 

   Factoring a polynomials having three terms of the form Ax² + Bx +C
         8x² - 10x - 3
   (I)  Find two number whose product is the first term (8x²) and place these factors in the left sides
         of the parentheses.     4x x 2x = 8x²
         (4x      )(2x       ) 

   (II) Find two number whose product is the last term (- 3) and place these factors in the right sides
         of the parentheses.     -3  x 1 = - 3
         (4x + 1)(2x - 3) 
       
   (III) Multiply inner terms (1 x 2x = 2x) and outer terms (4x x -3 = -12x) , add the result -12x +2x = -10x
            If  the result of  (III)  is equal to the middle term - 10x,  then (II) is the solution (4x + 1)(2x - 3)
            else repeat the process (I,II,III).

     8x² - 10x - 3 =  (4x + 1)(2x - 3)