How to factor 2x^2+x-15

(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)