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LogicalApple
 one year ago
Best ResponseYou've already chosen the best response.1You can use the rational roots theorem to guess and check the possible roots. You will find that (x + 2) and (x + 6) are factors of this polynomial. The other factor is (x^2  5). Can you obtain the rational roots from here?

evy15
 one year ago
Best ResponseYou've already chosen the best response.0yes but how did you get those numbers

LogicalApple
 one year ago
Best ResponseYou've already chosen the best response.1Using the Rational Roots Theorem (http://www.mathwords.com/r/rational_root_theorem.htm) you guess and check the possible values. The possible rational roots are + p/q where p are the factors of 60 and q are the factors of 1. I.e., the possible rational roots are + 1, +2, +4, +5, +6., etc... By guess and check we can try x = 1, x = 1, x = 2, x = 2 and x = 2. We find that x = 2 results in a 0. That means (x + 2) is a factor. Divide the original polynomial by (x + 2) to obtain a simpler polynomial of degree 3 and repeat the same steps to obtain the next factor.

LogicalApple
 one year ago
Best ResponseYou've already chosen the best response.1I repeated x = 2 twice by accident in the explanation above. Anyway, to show x = 2 results in a 0: (2)^4+8(2)^3+7(2)^240(2)60 = 16  64 + 28 + 80  60 = 0 So if x = 2, that means (x + 2) must be a factor of the original polynomial. Division yields (see attached file). Our new polynomial is x^3 + 6x^2  5x  30. We can use the same Rational Roots Theorem to determine the remaining possible rational root(s).
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