Question

How do you factor the trinomial `5a^2+7a+2`?

Answer 1

(a + 1)(5a + 2)

Explanation:

`y = 5a^2 + 7a + 2`.
Since a - b + c = 0, use shortcut. One factor is (a + 1) and the other is `(a + c/a = a + 2/5)`
`y = 5(a + 1)(a + 2/5) = (a + 1)(5a + 2).`

Reminder of Shortcut
1. When a + b + c = 0:
- Two real roots: 1 and `c/a`
- One factor is (x - 1) and the other is `(x - c/a)`.
2. When a - b + c = 0:
- Two real roots: -1 and `(-c/a)`
- One factor is (x + 1) and the other is `(x + c/a)`