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cubed polynomial

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cubed polynomial

I'm stuck on how to factor this:



The left hand side has a rational zero.

The basic approach to problems like this is educated guesswork. Start by observing that all the coefficients are positive, so that any real root (for factoring) must be negative. Since the coefficient of r^3 is 1 and all the others are integers, any rational root (the only way to factor easily) must be an integer. Finally the constant term is the product of all the roots, so the only possible integers are its (negative) integer factors (1,2,3,6). So try substituting -1, -2, -3, -6 for r and see which one gives you 0.

You will end up with (r+c)(quadratic), where c = one of the above (1,2,3,6).

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