I have a homework assignment and I am not sure what to do. What is the Rational Zero Test? List and find zeros of f(x) from function f(x)=x^3+9x^2+8x-60.
Since the leading coefficient is 1, the possible
rational zeros are the integer divisors of the numerical
term in absolute value.
The possible rational zeros are therefore the factors of 60
and their negatives.
±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60
So we start trying. We try 1:
x^3+9x^2+8x-60
1 | 1 9 8 -60
| 1 10 18
------------
1 10 18 -42
Nope! Remainder is -42, not 0.
We try 2.
2 | 1 9 8 -60
| 2 22 60
------------
1 11 30 0
Aha. 2 is a rational zero.
So the synthetic division tells us
we have factored the polynomial as
f(x)=x^3+9x^2+8x-60
f(x)=(x-2)(x^2+11x+30)
Now we can finish factoring that and get
f(x)=(x-2)(x+6)(x+5)
So the zeros are 2, -6, and -5
Edwin
