A General Note: Factoring a Trinomial with Leading Coefficient 1
A trinomial of the form
x2+bx+c can be written in factored form as
(x+p)(x+q) where
pq=c and
p+q=b.
Solution
We have a trinomial with leading coefficient
1,b=2, and
c=−15. We need to find two numbers with a product of
−15 and a sum of
2. In the table, we list factors until we find a pair with the desired sum.
Factors of −15 |
Sum of Factors |
1,−15 |
−14 |
−1,15 |
14 |
3,−5 |
−2 |
−3,5 |
2 |
Now that we have identified
p and
q as
−3 and
5, write the factored form as
(x−3)(x+5).