Use your calculator, synthetic division and the rational zeros test to find all the zeros of the given function and use them to write function in factored form. Show your synthetic division.
Note: a=1
p(x)=x^3-6x^2-x+30

Question

Use your calculator, synthetic division and the rational zeros test to find all the zeros of the given function and use them to write function in factored form. Show your synthetic division. 
Note: a=1
p(x)=x^3-6x^2-x+30

zehanz · Answer

If you try a few "simple" numbers, like 1, -1, 2, -2,  3, -3, you will see that 3 is a zero of p(x). This means you can factor out x-3. Synthetic division gives the remaining 2nd deg polynomial:

3  [ 1  -6   -1    30 ]
            3   -9  -30
---------------- +
      1   -3  -10   0

So now p(x) = (x-3)(x²-3x-10)

I'm sure you can get the other factors now ;)