according to the rational root theorem, which statement about $f(x)=66x^{4}-2x^{3}+11x^{2}+35$ is true?\nany…

according to the rational root theorem, which statement about $f(x)=66x^{4}-2x^{3}+11x^{2}+35$ is true?\nany rational root of $f(x)$ is a factor of 35 divided by a factor of 66.\nany rational root of $f(x)$ is a multiple of 35 divided by a multiple of 66.\nany rational root of $f(x)$ is a factor of 66 divided by a factor of 35.\nany rational root of $f(x)$ is a multiple of 66 divided by a multiple of 35.

according to the rational root theorem, which statement about $f(x)=66x^{4}-2x^{3}+11x^{2}+35$ is true?\nany rational root of $f(x)$ is a factor of 35 divided by a factor of 66.\nany rational root of $f(x)$ is a multiple of 35 divided by a multiple of 66.\nany rational root of $f(x)$ is a factor of 66 divided by a factor of 35.\nany rational root of $f(x)$ is a multiple of 66 divided by a multiple of 35.

Answer

Brief Explanations:

The Rational Root Theorem states that if a polynomial (f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0) has integer - coefficients ((a_n\neq0) and (a_0\neq0)), then any rational root (p/q) of the polynomial must satisfy that (p) is a factor of the constant term (a_0) and (q) is a factor of the leading - coefficient (a_n). In the polynomial (f(x)=66x^4−2x^3 + 11x^2+35), the leading coefficient (a_n = 66) and the constant term (a_0 = 35). So any rational root of (f(x)) is of the form (p/q) where (p) is a factor of 35 and (q) is a factor of 66.

Answer:

Any rational root of (f(x)) is a factor of 35 divided by a factor of 66.