SOLUTION: 4.6 The following function is given. f(x)=x^3 -5x^2 -9x+45 a. List all rational zeros that are possible according to the Rational Zero Theorem: b. Use synthetic divisio

Question 1013833: 4.6
The following function is given.
f(x)=x^3 -5x^2 -9x+45
a. List all rational zeros that are possible according to the Rational Zero Theorem:
b. Use synthetic division to test several possible rational zeros in order to identify one actual zero
One rational zero of the given function is:
c. Use the zero from part (b) to find all the zeros of the polynomial function
The zeros of the function f(x)=x^3-5x^2 -9x+45 is:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^3 -5x^2 -9x+45=0
rational zeros are +/- 1,3,5,9,15,and 45, the factors of the constant divided by the factors of x^3.
using synthetic division with 3. By looking at the division, 1 did not look like it would work, so I went to 3. If that didn't work, I would try -3. Then I would try 5 or -5.
1;;;;-5;;;;-9;;;;-45
1;;;;-2;;;;-15---0
Therefore,(x-3) is a factor, and what is left over is x^2-2x+15. That factors to (x-5)(x+3).
roots are -3,3, and 5.

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