SOLUTION: Using synthetic division, find one zero of the polynomial f(x)=x^3-21x-20 then write the polynomial in factored form based on the zero you found: Zero for this polynomial: f(___)=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Using synthetic division, find one zero of the polynomial f(x)=x^3-21x-20 then write the polynomial in factored form based on the zero you found: Zero for this polynomial: f(___)=      Log On


   

Question 1182627: Using synthetic division, find one zero of the polynomial f(x)=x^3-21x-20 then write the polynomial in factored form based on the zero you found:
Zero for this polynomial: f(___)=0
Factors of the polynomial based on the above zero: f(x)=
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The potential zeros have numerators which are divisors of the last term in
absolute value, 21 and denominators which are divisors of the leading
coefficient 1.  So all potential divisors are: 

  

Try 1

1 | 1 0 -21 -20
  |   1   1 -20 
    1 1 -20 -40

That left remainder -40, not 0, so we try the next one, -1

-1 | 1  0 -21 -20
   |   -1   1  20 
     1 -1 -20   0

That left remainder 0, so -1 is a zero, and (x+1) is a factor.
The other three numbers on the bottom row give us the coefficients
of the other factor, (1x2-1x-20).  So f(x) factors as

f%28x%29=%28x%5E%22%22%2B1%29%28x%5E2-x-20%29

We can further factor the quadratic in the second parentheses:

f%28x%29=%28x%5E%22%22%2B1%29%28x%5E%22%22-5%29%28x%5E%22%22%2B4%29

The zeros of f(x) are found by setting each factor = 0

x+1=0 ;  x-5=0;  x+4=0
  x=-1;    x=5     x=-4

The graph shows that these three zeros are at the 3 x-intercepts:

graph%28400%2C400%2C-10%2C10%2C-60%2C20%2C+x%5E3-21x-20%29


Edwin