Math Problem?

Question

The Rational Zeros Therem is used to find a list of possibilities for rational zeros for a polynomial. Use the Rational Zeros Theorems to determine which of the following numbers is on the list of possibilities for rational zeros of
P(x) = 6x^3 - x^2 + 3x - 4

A. -3/2
B. -1/6
C. 6
D. 24

Answer 1

Recall that the Rational Zero Theorem states that all rational zeros of a polynomial must be in the form of a ratio of the constant term and highest-order coefficient. Thus, all zeros to the given polynomial are in the ratio a/b, where a is a factor of 4 (or -4), and b is a factor of 6 (-6).

A: 3 is not a factor of 4. Discarded.
B: A possibility, because 1 is a factor of 4 and 6 is a factor of 6.
C: 6 is not a factor of 4. Discarded.
D: 24 is not a factor of 4. Discarded.

-1/6 (B) is the only possibility of the ones that were given.

(EDIT: By the way, the first two answers given are wrong.)

Answer 2

B. -1/6

Look for fractions of the form {divisors of the constant term} / {divisors of the leading coeff},

which in your case is -4/6 (so look for DIVISOR OF 4 / DIVISOR OF 6).

The Rational Zeros Therem says every rational zero of a polynomial with integer coefficients has the form
p/q
where p and q have no common factors other than 1, and

p = a factor of the constant term

q = a factor of the leading coefficient .

Hope this helps.

Answer 3

B [-1/6] is POSSIBLE rational zero. The rest are not.

Possible rational zeros are of the form p/q where p is an integer divisor of the constant (4, in your case) and q is an integer divisor of the conefficient of the highest degree term (6 in your problem).

Answer 4

Only B can be listed becaus if p/q( in its lowest terms) is a rational root
p must divide 4 and q must divide 6

Answer 5

factors of leading coeff 2,3
factors of constant 2

A could be, B can't , C could be, D cant