SOLUTION: Hello! What are the rational zeros of this function? Please explain each step. f(x) = x^3 � 21x � 20 Thank you

Question 976975: Hello!
What are the rational zeros of this function? Please explain each step.
f(x) = x^3 � 21x � 20
Thank you
Found 2 solutions by lwsshak3, rothauserc:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
What are the rational zeros of this function? Please explain each step.
f(x) = x^3 � 21x � 20
***
use rational roots theorem with synthetic division:
...0...|.....1......0......-21.......-20.......
.-1...|.....1.....-1......-20........0. (-1 is a zero)
f(x)=(x+1)(x^2-x-20)
f(x)=(x+1)(x+4)(x-5)
rational zeros are: -1, -4, and 5
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
f(x) = x^3 � 21x � 20
I always like to try x = 1 or -1 as a first step
f(-1) = -1 + 21 - 20 = 0, and
(x + 1) is a factor of f(x)
now we can apply synthetic division
-1 | 1 0 -21 -20 |
note: the 0 represents the x^2 coefficient since there is no x^2 in f(x)
| -1 1 20 |
| 1 -1 -20 0 |
the result is
x^2 -x -20
this polynomial can be factored
(x-5)(x+4)
therefore the complete factorization is
(x+1)(x-5)(x+4) and
our zeros are -1, 5, -4

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