[MOVED] Long Division with polynomials

[Guest]

I'm not really sure about this question. To divide or find factors of polynomials, do I use "f(x) = d(x)q(x) + r(x)" to some how find the other factors? Or just play with the numbers? I asked a couple of my friends but we don't know how to start it. Thanks so much in advance for any help.

Here's the question:

One factor of x³ + 3x² - 16x + 12 is x-2. Find all factors.

 

[galactus]

Do you know how to long divide polynomials?.

Since we are told that x-2 is a factor:

      x^2+5x-6
     ------------------------------------
x-2|x^3+3x^2-16x+12
    x^3-2x^2
     ---------------------------
       5x^2-16x+12
       5x^2-10x
          -------------------------
           -6x+12
           -6x+12
          ----------------------
                  0

When you divide you get \(\displaystyle x^{2}+5x-6\)

Now, factor this quadratic and you'll have your other 2 factors?. See?

 

[Guest]

Ohhh! Thank you so so much, i understand it now. I was way, way off.. Thanks again!