Question

Question 1
3 x² - 4x-3=0​

Answer 1

   Factoring  x2-4x+3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  +3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 3 = 3  

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   -4 .

     -3    +    -1    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  -1  

                    x2 - 3x - 1x - 3

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

                   x • (x-3)

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

                    1 • (x-3)

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

                   (x-1)  •  (x-3)

            Which is the desired factorization