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LogicalAppleBest ResponseYou've already chosen the best response.1
You 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?
 one year ago

evy15Best ResponseYou've already chosen the best response.0
yes but how did you get those numbers
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
Using 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.
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
I 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).
 one year ago
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