Question

Which of the binomial is a factor of 6x2 - x - 1?Which of the binomial is a factor of 6x2 - x - 1?

Answer 1

Factoring  6x2-x-1 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -1 = -6 

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -1 .

     -6   +   1   =   -5     -3   +   2   =   -1   That's

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  2 

                     6x2 - 3x + 2x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

                    3x • (2x-1)

              Add up the last 2 terms, pulling out common factors :

                     1 • (2x-1)

Step-5 : Add up the four terms of step 4 :

                  Final Answer is  (3x+1)  •  (2x-1)

 Which is the desired factorization