SOLUTION: Can you please help me divide f(x)=3x^3-16x^2-103x+36 when (x+4)is a factor. I've done the synthetic division to get f(x)= (x+4)(3x^2-28x+9) but I'm stuck on how to factor (3x^2-28

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me divide f(x)=3x^3-16x^2-103x+36 when (x+4)is a factor. I've done the synthetic division to get f(x)= (x+4)(3x^2-28x+9) but I'm stuck on how to factor (3x^2-28      Log On


   

Question 698834: Can you please help me divide f(x)=3x^3-16x^2-103x+36 when (x+4)is a factor. I've done the synthetic division to get f(x)= (x+4)(3x^2-28x+9) but I'm stuck on how to factor (3x^2-28x+9).
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
 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