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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 truethe O Any rational root of foo a factor of 35 divided by a factor of 66is A class=

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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-

[tex]a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0[/tex]

If [tex]a_{0}[/tex] and [tex]a_{n}[/tex] are nonzero, then each rational solution x will be,

[tex]x=\pm \dfrac{\text{Factors of }a_0}{\text{Factors of }a_n}[/tex]

The given polynomial is,

[tex]66x^4-2x^3+11x^2 +35[/tex]

Here,

[tex]a_{0}=35[/tex] and [tex]a_{n}=66[/tex]

Applying the theorem,

[tex]x=\pm \dfrac{\text{Factors of }35}{\text{Factors of }66}[/tex]

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:

[tex]P(x)=66x^4-2x^3+11x^2+35[/tex]

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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