Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18?
(x − 3)
(x + 3)
(x − 1 over 3)
(x + 1 over 3)

I know the answer is (x-3), I just want to know if there is an easier and more reliable way of getting the answer than checking each answer choice to see if it works because when I first did this problem, I accidentally divided incorrectly and thought (x-3) was wrong. I found out about my mistake later, but the explanation I received was to use the rational roots test and plug in all 24 possible values until I get the three that work. Is there an easier way?

Question

Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18?
(x − 3)
(x + 3)
(x − 1 over 3)
(x + 1 over 3)

I know the answer is (x-3), I just want to know if there is an easier and more reliable way of getting the answer than checking each answer choice to see if it works because when I first did this problem, I accidentally divided incorrectly and thought (x-3) was wrong. I found out about my mistake later, but the explanation I received was to use the rational roots test and plug in all 24 possible values until I get the three that work. Is there an easier way?

anonymous · Answer

$$(x-3) (x+6) (4 x-1) $$

greenbannanabob · Answer

But how do you get (x−3)(x+6)(4x−1)?

mathmale · Answer

Are you familiar with synthetic division?  If so, that method is one of the fastest you could use to determine whether a given expression (binomial) is actually a divisor of the given polynomial.

anonymous · Answer

You request Mathematica to factor 4x3 + 11x2 − 75x + 18

mathmale · Answer

Robert, yes, but students are most often required to use traditional methods to factor polynomials.  Mathematica would make a great check, after the grunt work has been completed.

rebeccaxhawaii · Answer

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