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

Explanation:

Step1: Recall Rational Root Theorem

For a polynomial (a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0), the possible 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_0) and (a_n) in (f(x))

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).

Step3: Determine possible rational roots

By the Rational Root Theorem, the possible rational roots of (f(x)) are of the form (\frac{p}{q}), where (p) is a factor of (35) and (q) is a factor of (66). That is, any rational root of (f(x)) is a factor of (35) divided by a factor of (66).

Answer:

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