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

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

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 \frac{\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 \frac{\text{Factors of }35}{\text{Factors of }66}`

Answer 2

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

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.