Question

How do you factor completely: `2x^2 + 13x + 15`?

Answer 1

`2(x + 3/2)(x + 5)`

Explanation:

`ax^2 + bx + c = a(x - x_1)(x - x_2)`

`2x^2 + 13 x + 15 = 0`

`x_i = (- 13 ± sqrt{13^2 - 4 * 2 * 15}) / 4`

`x_1 = (-13 + 7)/4 = -3/2`

`x_2 = (-13 -7)/4 = -5`

Answer 2

Factor y = 2x^2 + 13x + 15

Explanation:

I use the new AC Method to factor trinomials (Google, Yahoo Search).
`y = 2x^2 + 13x + 15 =` 2(x - p)(x - q)
Converted `y' = x^2 + 13x + 30 =`(x - p')(x - q').
Factor pairs of ac = 30 -> (2, 15)(3, 10). this sum is 13 = b.
Then, p' = 3 and q' = 10.
Then, `p = 3/2` and `q = 10/2 = 5.`
Factored form: `y = 2(x + 3/2)(x + 5) = (2x + 3)(x + 5)`