Question

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?

Answer 1

Using the factor theorem, it is found that the polynomial is:

$f(x) = x^3 - 2x^2 - 3x + 6$

Given by the first option

---------------------------

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ using the factor theorem it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$, in which a is the leading coefficient.

---------------------------

In this question:

• $x_1 = 2$
• $x_2 = \sqrt{3}$
• $x_3 = -\sqrt{3}$
• By the options, leading coefficient $a = 1$

Thus:

$f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})$

$f(x) = (x - 2)(x^2 - 3)$

$f(x) = x^3 -2x^2 - 3x + 6$

Which is the polynomial.

A similar problem is given that: brainly.com/question/4786502