Question 624140: Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x^3 - 4x^2 + 7x - 8 = 0. Do not find the actual roots.
A. –8, –1, 1, 8
B. –8, –4, –2, –1, 1, 2, 4, 8
C. 1, 2, 4, 8
D. no possible roots
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! The possible rational roots of any polynomial are all the ratios, positive and negative, that can be formed using a factor of the constant term in the numerator and a factor of the leading coefficient in the denominator.
The constant term is the term that has no variables. Normally polynomials are written with the terms in order from highest exponent to lowest. In this order, the constant term will be at the end. Your constant term is -8.
The leading coefficient is the coefficient of the term with the highest exponent. If the polynomial is in normal order, the the leading coefficient will be the first coefficient because the term with the highest exponent is first. Your leading coefficient is 1. (Remember, an "invisible" coefficient is a coefficient of 1.)
As far as the answer to your problem goes...
D cannot be correct. Every polynomial will have some possible rational roots.
C cannot be correct. It has no possible negative roots. If 1, 2,4 and 8 are possible rational roots, then so would -1, -2, -4 and -8.
I'll leave it up to you to figure out if the answer is A or B. Just remember, the list should include "all the ratios, positive and negative, that can be formed using a factor of the constant term in the numerator and a factor of the leading coefficient in the denominator."
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