Use the graph of the polynomial function to find the factored form of
its related polynomial. Assume it
has no constant factor

The factored form of the polynomial is .

Step-by-step explanation:

According to the graph, we have a second order polynomial with a vertical axis of symmetry. The standard form of the polynomial is:

(1)

Where:

- Independent variable.

- Dependent variable.

, , - Coefficients.

We can obtain the solution of the polynomial by knowing three distinct points. From graph we know that the curve pass through the following three points: , , . Three linear equations are constructed:

(2)

(3)

(4)

The solution of this system is , and . Then, the polynomial in standard form is . By factorization, we find that factored form is:

(5)

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

the first option is the answer.