Question

How do you factor `3x^2-13x+4`?

Answer 1

You can find its roots and then turn them into factors.

Using Bhaskara to find the roots:

`(13+-sqrt(169-4(3)(4)))/6`
`(13+-11)/6`
`x_1=4`, which is the same as the factor `x-4=0`
`x_2=1/3`, which is the same as the factor`3x-1=0`

Factoring your quadratic function, then:

`3x^2-13x+4=(x-4)(3x-1)`

Answer 2

There is another way. I use the new AC Method (Google, Yahoo Search) to factor trinomials

y = 3x^2 - 13x + 4 = (x - p)( - q)

Converted function: f'(x) = x^2 - 13x + 12.= (x - p')(x -q')

Compose factor pair of 12: (1, 12). This sum is 12 + 1 = 13 = -b.

Then p' = -1 and q' = -12.

Consequently, p = (p')/a = -1/3 and q' = (q')/a = -12/3 = -4

Factored form of y: y = (x - 1/3)(x - 4) = (3x - 1)(x - 4).