# How do you factor 12f² +35f +8?

##### 2 Answers

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:

That is

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** . **Case 1** . Compose factor pairs of (a.c) and find the pair whose sum is (b), or -b. Next find p = (p')/a and q = (q')/a.

This new AC Method is fast, systematic, no factoring by grouping, and no solving binomials.