How to do this question?

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1 Answer
Feb 24, 2018

See below

Explanation:

Rational root theorem states that rational roots of a polynomial will take the form of p/q where p is a factor of the constant term and q is a factor of the leading coefficient. So, for f(x)=12x^3+20x^2-x-6

p={1,2,3,6}
q={1,2,3,4,6,12}

p/q={+-1,+-1/2,+-1/3,+-1/4,+-1/6,+-1/12,+-2,+-2/3,+-3,+-3/2,+-3/4,+-6} (take each value of p and divide it by each and every value of q)

Now, theoretically, we would test each of these p/q values to find which ones are actually zeros of the function f(x)=12x^3+20x^2-x-6

Truthfully, what you can do is find the rational zeros in your calculator and prove that they are zeros by using traditional or synthetic substitution. Once you know a root, the factor is (x-a) where a is your root.