Zeros of a Polynomial Function

Question

Determine all the real zeros of f(x)= x⁴-x³-5x²+3x+6 

 

I'm not sure how this would be factored out, thank you in advance

Answer 1

Katie

 

You would use synthetic division in this case and I hope you learned how to do that.  You know you have up to 4 roots since the highest exponent is 4 and that you have both positive and negative roots because of the switches from positive to negative from one term to the next.  I always like to start with -1 as a root, ie (x+1)

 

 

-1    |  1  -1  -5  3  6 

       |

          1  -2  -3  6  0

 

 

It works out nicely leaving you with (x+1)(x³-2x²  -3x+6)

 

You can do the same with your 3rd order polynomial with root 2 and it leaves you with (x² -3)

 

Finally (x² -3)(x+1)(x-2)

 

You can foil it back to make sure I did the signs right and that it works out.

 

Good luck,

Lori