Question

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

Answer 1

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 2

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.