Question

Factor the trinomial 2x2 + 17x - 9

Answer 1

Factoring a trinomial of the form ax^2 + bx + c
Step 1. Multiply ac
In this case, ac = 2 * (-9) = -18
Step 2. Find two factors of ac that add up to b. Call them p and q.
In this case, find two factors of -18 that add up to 17.
They are 18 and -1.
Step 3. Break the middle term, bx, into two terms, px + qx.
Here you'll get
2x^2 + 18x - x - 9
Step 4. Factor by parts. Take a common factor out of the first two terms. Take a common factor out of the last two terms.
Here you'll have:
2x(x + 9) - 1(x + 9)
Step 5. Factor out the common factor.
(x + 9)(2x - 1)