How do you factor 12f² +35f +8?
To find this, notice that
The determinant of this quadratic is given by the formula:
Being a perfect square, the quadratic has zeros for rational values of f given by the formula:
These values correspond to the factors
I use the new AC Method (Google, Yahoo Search) to factor trinomials.
y = 12x^2 + 35x + 8 = (x - p)(x - q)
Converted trinomial: (a.c = 96)
y' = x^2 + 35x + 96 = (x - p')(x - q'). Find 2 numbers p' and q' that product = ac = 96 and sum = b = 35.
Compose factor pairs of 96 ->(2, 48)(3, 32). This sum is 35 = b.
Then, p' = 3 and q' = 32
Then, p = p'/a = 3/12 = 1/4, and q = q'/a = 32/12 = 8/3
Factored form: f(x) = (x - p)(x - q) = (x + 1/4)(x + 8/3) = (4x + 1)(3x + 8)
Summary of the new AC Method .
CASE 1 .
CASE 2 .
This new AC Method is fast, systematic, no factoring by grouping, and no solving binomials.