<PRE><B>Question 658208</B>
Factors of 15: 1, 3, 5, 15, -1, -3, -5, -15


Factors of 1: 1, -1


*** Note: Include negative factors as well ***


Divide all the factors of 15 by the factors of 1


Potential rational roots of x^3-x^2-7x+15: 


1, -1, 3, -3, 5, -5, 15, -15


Note: there are 8 possible rational roots for x^3-x^2-7x+15.



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Check to see if x = 1 is a root for x^3-x^2-7x+15:


(1)^3-(1)^2-7(1)+15 = 8


Since the result is NOT 0, x = 1 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = -1 is a root for x^3-x^2-7x+15:


(-1)^3-(-1)^2-7(-1)+15 = 20


Since the result is NOT 0, x = -1 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = 3 is a root for x^3-x^2-7x+15:


(3)^3-(3)^2-7(3)+15 = 12


Since the result is NOT 0, x = 3 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = -3 is a root for x^3-x^2-7x+15:


(-3)^3-(-3)^2-7(-3)+15 = 0


Since the result is 0, x = -3 is a root for x^3-x^2-7x+15.



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Check to see if x = 5 is a root for x^3-x^2-7x+15:


(5)^3-(5)^2-7(5)+15 = 80


Since the result is NOT 0, x = 5 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = -5 is a root for x^3-x^2-7x+15:


(-5)^3-(-5)^2-7(-5)+15 = -100


Since the result is NOT 0, x = -5 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = 15 is a root for x^3-x^2-7x+15:


(15)^3-(15)^2-7(15)+15 = 3060


Since the result is NOT 0, x = 15 is NOT a root for x^3-x^2-7x+15.



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Check to see if x = -15 is a root for x^3-x^2-7x+15:


(-15)^3-(-15)^2-7(-15)+15 = -3480


Since the result is NOT 0, x = -15 is NOT a root for x^3-x^2-7x+15.



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So the polynomial x^3-x^2-7x+15 has exactly one rational root and it is x = -3.



So the only rational factor is  (x + 3)



Since the degree is 3, there are 2 other roots. These two other roots are either irrational or complex roots.


Use polynomial long division, then use the quadratic formula to figure out what type of roots these other two roots are (I&#39;ll let you do this).
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