Question

Give the possible expression for the length and breadth of the rectangle whose area is 6a2+a-12

Answer 1

  Factoring  6a2-a-12 

The first term is,  6a2  its coefficient is  6 .
The middle term is,  -a  its coefficient is  -1 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -12 = -72 

Step-2 : Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -1 .

     -72   +   1   =   -71     -36   +   2   =   -34     -24   +   3   =   -21     -18   +   4   =   -14     -12   +   6   =   -6     -9   +   8   =   -1   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  8 
                     6a2 - 9a + 8a - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3a • (2a-3)
              Add up the last 2 terms, pulling out common factors :
                    4 • (2a-3)
Step-5 : Add up the four terms of step 4 :
                    (3a+4)  •  (2a-3)
             

(2a - 3) • (3a + 4) = 0 is the expression