Final answer to the problem
$z+8+\frac{12}{z-3}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- Write in simplest form
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Let's divide the polynomial by $z-3$ 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 ($1$) and multiply it by the root of the denominator ($3$). Add the result to the second coefficient and multiply this by $3$ and so on
$\left|\begin{matrix}1 & 5 & -12 \\ & 3 & 24 \\ 1 & 8 & 12\end{matrix}\right|3$
2
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 ($12$) divided by the divisor
$z+8+\frac{12}{z-3}$
Final answer to the problem
$z+8+\frac{12}{z-3}$