According to the rational root theorem, which statement about f(x) = 66x4 – 2x3 + 11x2 + 35 is true? any rational root of f(x) is a factor of 35 divided by a factor of 66. any rational root of f(x) is a multiple of 35 divided by a multiple of 66. any rational root of f(x) is a factor of 66 divided by a factor of 35. any rational root of f(x) is a multiple of 66 divided by a multiple of 35.

The correct statement is any rational root of f(x) is a factor of 35 divided by a factor of 66

Step-by-step explanation:

The correct option is  Any rational root of f(x) is a factor of 35 divided by a factor of 66

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the  leading coefficient of the function.

f(x)=66x4 – 2x3 + 11x2 + 35

Here 66 is the factor of the leading coefficient(q)

and 35 is the factor of the constant term(p)

Thus p/q = 35/66

Therefore the correct statement is any rational root of f(x) is a factor of 35 divided by a factor of 66

A

Step-by-step explanation:

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