problem:
list all of the possible zeros of each function
h(x)=x^(3)-5x^(2)+2x+12
answer pwease and explanation ! thank u (:

Question

problem: 
list all of the possible zeros of each function
h(x)=x^(3)-5x^(2)+2x+12
answer pwease and explanation ! thank u (:

anonymous · Answer

Rational Zeros Theorem. If you have any polynomial with integer coefficients, $$a_{n}x^n+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}=0$$ all the rational zeros will be of the form p/q, where p is a factor of a0, and q is a factor of an. So if p/q is a zero, there is a corresponding factor, (qx-p).  In your example the candidates for rational zeros are: plus and minus 12/1, 6/1, 4/1, 3/1 and 2/1  
From here, you can use synthetic division (or long division) on the candidate zeros until you find one that leaves you with no remainder.  Testing 4/1=4|dw:1332516857212:dw| If we got a remainder of zero, x-4 would have been a factor of this polynomial.  Since we have a remainder, it is not.  Keep going until you find a linear factor of this cubic.  Then you are left with the product of a linear factor and a quadratic factor.  The quadratic function will also need to be factored as usual.  Once you have your three factors, your zeros are found by taking each one separately, setting it equal to zero, and solving for x.