factor the trinomial 2w^2 - w – 36

Ans:

This is of the form ax^2 + bx+ c with a != 0 and a!= 1
let

ax^2 + bx + c = (mx + n)(px + q) = mn x^2 + (mq+pn) x + nq
b is split into mq+pn and product = mqpn = ac

using that we multiply 2 and -36 to get -72

now 2 numbers to be chosen that product = 72 and sum = -1 (coefficient of w) they are 8 and - 9

so 2w^2 - w - 36 = 2w^2 + 8w - 9w - 36 = 2w(w+4) - 9(w+4) = (w+4)(2w-9)