To solve the problem we must know about the Remainder Theorem.
<h3>What is the Remainder theorem?</h3>
According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
The roots of the function are 2, 1, and -2.
Given to us
- One factor of f (x) = is (x – 2).
<h3>What is the quotient of the function?</h3>
We know (x-2) is the factor of the function, f(x) = ,
therefore,
As (x-2) is the factor of the function, therefore, the remainder will be zero for the equation,
<h3>What are the factors of the function?</h3>
Solving the quadratic equation,
Hence, the roots of the function are 2, 1, and -2.
Learn more about Remainder theorem:
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