f(x)= (x + 4)(3x² - 28x + 9)

You need to factor 3x² - 28x + 9

There is only one way to factor 3x², as 3x times x
So write this:

    (3x    )(x    )

There are 3 ways to factor the 9, as 3*3,1*9 and 9*1

    (3x   3)(x   3)   

    (3x   1)(x   9)

    (3x   9)(x   1)

If you test those using FOIL, thinking that the two signs
have to be negative, it doesn't take long to see that

    (3x - 1)(x - 9)    

is the way to factor it, so

  f(x)= (x + 4)(3x - 1)(x - 9)

Edwin