SOLUTION: One factor of x^3+x^2-14x-24 is (x-4). Find the remaining zeros.

Algebra ->  Rational-functions -> SOLUTION: One factor of x^3+x^2-14x-24 is (x-4). Find the remaining zeros.      Log On


   

Question 188148This question is from textbook algebra2
: One factor of x^3+x^2-14x-24 is (x-4).
Find the remaining zeros. This question is from textbook algebra2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since (x-4) is a factor, this means that x=4 is a root (or zero) of x%5E3%2Bx%5E2-14x-24

Now set up a synthetic division table by placing the zero 4 and the coefficients of x%5E3%2Bx%5E2-14x-24 along the top row. Perform synthetic division to get: 

 4 |1   1   -14   -24
   |    4    20    24
   -------------------
    1   5     6     0



Since the remainder is 0, this means that 4 is a root.


The first three numbers in the bottom row form the quadratic: x%5E2%2B5x%2B6


Now solve x%5E2%2B5x%2B6=0 to find the other 2 solutions.