Question

Which expression is equivalent to 6x² - 7x-20 ?

Answer 1

Answer:

(3x+4)(2x−5)

Step-by-step explanation:

The first term is,  6x2  its coefficient is  6 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  -20

Step-1 : Multiply the coefficient of the first term by the constant   6 • -20 = -120

Step-2 : Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -7 .

     -120    +    1    =    -119

     -60    +    2    =    -58

     -40    +    3    =    -37

     -30    +    4    =    -26

     -24    +    5    =    -19

     -20    +    6    =    -14

     -15    +    8    =    -7    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  8

                    6x2 - 15x + 8x - 20

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

                   3x • (2x-5)

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

                   4 • (2x-5)

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

                   (3x+4)  •  (2x-5)

            Which is the desired factorization