use the rational root theorem to list all possible rational roots of the polynomial equation x^3-x^2-3=0 DONT FIND THE ACTUAL ROOTS
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Okay so first is what is a Rational Root Theorem?
Do you know q and p?
q is the leading coefficient and p is the last coefficient.
Find the factors of each and divide each p with each q
Follow the steps...
1. Find the factors of p (3) - the last digit/coefficient
2. Find the factors of q (1) - the number in front of the first x
3. Divide each p factors with 1 factors (1/1 and 3/1)
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I am confused..
Okay... Wanna go over step by step?
Rational Root Theorem tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.
Just remember that the last term, which in this case is -3 is P
and the first term, which in this case is 1 because the first term is only x is Q
Step by step?
Sorry if I a taking time.. I am helping 10 people at once.
3 is p
1 is q
factors of 3: 1, 3
factors of 1: 1
(+-) 1/1 and 3/1
With these numbers, use the "Synthetic Division" to find which of these two is a possible rationale root of the polynomial.
What is synthetic division
Pardon the drawing.. I used my mouse track pad
that type of thing is called synthetic division. Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.