Question

How to factor 2x^2+x-15

Answer 1

Answer:

(2x - 5) • (x + 3)

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   2 • -15 = -30

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   1 .

     -30    +    1    =    -29

     -15    +    2    =    -13

     -10    +    3    =    -7

     -6    +    5    =    -1

     -5    +    6    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  6

                    2x2 - 5x + 6x - 15

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

                   x • (2x-5)

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

                   3 • (2x-5)

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

                   (x+3)  •  (2x-5)

            Which is the desired factorization

Final result :

 (2x - 5) • (x + 3)