Respuesta :
Answer:
f (x) = x3 – 3x2 – 5x + 15
Step-by-step explanation:
i just took the test
The required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]
The correct answer is an option (C)
What is polynomial?
"It is an algebraic expression that consist of variables and coefficients."
What is a factor theorem?
- "It describes the relationship between the root of a polynomial and a factor of the polynomial."
- "This theorem states that - If f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x - a) is a factor of f(x), if f(a) = 0"
For given question,
The polynomial function has the zeros 3, radical 5, and negative radical 5.
The polynomial function has zeros 3, √5, -√5
This means the factors of the polynomial function are (x - 3), (x - √5) and (x - (-√5)) = (x + √5).
Using the Factor theorem the polynomial function would be,
[tex]\Rightarrow f(x)=0\\\\\Rightarrow (x - 3)\times (x - \sqrt{5} )\times (x + \sqrt{5} ) = 0\\\\\Rightarrow (x-3)\times (x^{2} - (\sqrt{5} )^{2} )=0\\\\\Rightarrow (x-3)\times (x^{2} - 5)=0\\\\\Rightarrow x \times (x^{2} - 5) - 3\times (x^{2} - 5) =0\\\\\Rightarrow x^{3}-5x-(3x^{2}-15)=0\\\\\Rightarrow x^{3}-3x^{2}-5x+15=0[/tex]
Therefore, the required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]
The correct answer is an option (C)
Learn more about the factors of the polynomial here:
https://brainly.com/question/26354419
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