Final answer to the problem
Step-by-step Solution
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Let's divide the polynomial by $x-4$ using synthetic division (also known as Ruffini's rule). First, write all the coefficients of the polynomial in the numerator in descending order based on grade (putting a zero if a term doesn't exist). Then, take the first coefficient ($5$) and multiply it by the root of the denominator ($4$). Add the result to the second coefficient and multiply this by $4$ and so on
In the last row appear the new coefficients of the polynomial. Use these coefficients to rewrite the new polynomial with a lower grade, and the remainder ($239$) divided by the divisor