according to the rational root theorem, which statement about (f(x)=12x^{3}-5x^{2}+6x + 9) is true?\nany…

according to the rational root theorem, which statement about (f(x)=12x^{3}-5x^{2}+6x + 9) is true?\nany rational root of (f(x)) is a multiple of 12 divided by a multiple of 9.\nany rational root of (f(x)) is a multiple of 9 divided by a multiple of 12.\nany rational root of (f(x)) is a factor of 12 divided by a factor of 9.\nany rational root of (f(x)) is a factor of 9 divided by a factor of 12.

according to the rational root theorem, which statement about (f(x)=12x^{3}-5x^{2}+6x + 9) is true?\nany rational root of (f(x)) is a multiple of 12 divided by a multiple of 9.\nany rational root of (f(x)) is a multiple of 9 divided by a multiple of 12.\nany rational root of (f(x)) is a factor of 12 divided by a factor of 9.\nany rational root of (f(x)) is a factor of 9 divided by a factor of 12.

Answer

Answer:

Any rational root of (f(x)) is a factor of 9 divided by a factor of 12.

Explanation:

Step1: Recall Rational Root Theorem

For a polynomial (a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0), rational roots are of the form (\frac{p}{q}), where (p) is a factor of the constant term (a_0) and (q) is a factor of the leading - coefficient (a_n).

Step2: Identify (a_n) and (a_0)

In (f(x)=12x^3 - 5x^2+6x + 9), (a_n = 12) and (a_0 = 9).

Step3: Determine rational roots form

By the Rational Root Theorem, the rational roots of (f(x)) are of the form (\frac{p}{q}), where (p) is a factor of 9 and (q) is a factor of 12. So any rational root of (f(x)) is a factor of 9 divided by a factor of 12.