Concept explainers
Divide a polynomial
To calculate: Whether
Answer to Problem 1P
Solution: Yes,
Explanation of Solution
Given Information:
Provided Polynomial is
Formula used:
One of the approaches to find the roots of a polynomial is represented by the pseudo code. The pseudo code performs the division of an
order polynomial by a monomial factor
:, if the monomial is one of the root of the equation then the remainder becomes
Calculation:
Consider the provided expression:
Consider the monomial factor
For the polynomial provided in the question
,
,
, and
Follow the approach provided by following Pseudo code.
Here,
Iterate the root in the following interval:
. For
For
For
For
The remainder of zero. Thus, 2 will be a root of the provided polynomial.
To verify the pseudo code, write a MATLAB program and execute it:
Execute the code following result will be obtained:
Thus, the remainder is
and quotient is
Therefore, the term
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