Find a formula for the given polynomial.

In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:

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

Equation of a polynomial, according to it's zeros:

Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.

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

Identifying the zeros:

Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:

Thus

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

Leading coefficient:

Passes through point (2,-8), that is, when , which is used to find a. So

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

Considering the zeros and the leading coefficient, the formula is:

A similar problem is found at

The formula that represents the polynomial in the figure is .

Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that . By Algebra we understand that polynomial can be represented in this manner known as Factorized form:

(1)

Where:

- Grade of the polynomial.

- Index of the root binomial.

- Independent variable.

We notice that polynomials has three roots in , and , having the following construction:

The formula that represents the polynomial in the figure is .

Here is a question related to the determination polynomials:

560

hope this : )