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According to Rational Root Theorem, which statement about fox) 66x4 2x3 11x2 +35 is true?the O Any rational root of foo) a factor of 35 divided by a factor of 66.is Any rational root of f(x) is a multiple of 35 divided by a multiple of 66Any rational root of f() 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

According to Rational Root Theorem, which statement about fox) 66x4 2x3 11x2 +35 is true?the O Any rational root of foo) a factor of 35 divided by a factor of 6 class=

Verified Answer :

InesWalston

Answer:

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

Step-by-step explanation:

Rational Root Theorem-

\(a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0\)

If \(a_{0}\) and \(a_{n}\) are nonzero, then each rational solution x will be,

\(x=\pm \dfrac{\text{Factors of }a_0}{\text{Factors of }a_n}\)

The given polynomial is,

\(66x^4-2x^3+11x^2 +35\)

Here,

\(a_{0}=35\) and \(a_{n}=66\)

Applying the theorem,

\(x=\pm \dfrac{\text{Factors of }35}{\text{Factors of }66}\)

Answer:

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

Step-by-step explanation:

The Rational Root Theorem states that:

If P(x) is a Polynomial with integer coefficients and if there exist a rational root of the polynomial i.e. of the form p/q then p is the factor of the constant term and q is a factor of leading coefficient of the polynomial function P(x).

Here we have:

\(P(x)=66x^4-2x^3+11x^2+35\)

So, according to the Rational Root Theorem the statement that holds true is:

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

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