Exercise

$\frac{x^3+7x^2+4}{x+7}$

Step-by-step Solution

1

Let's divide the polynomial by $x+7$ 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 ($-7$). Add the result to the second coefficient and multiply this by $-7$ and so on

$\left|\begin{matrix}1 & 7 & 0 & 4 \\ & -7 & 0 & 0 \\ 1 & 0 & 0 & 4\end{matrix}\right|-7$
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 ($4$) divided by the divisor

$x^{2}+0x+\frac{4}{x+7}$
3

Any expression multiplied by $0$ is equal to $0$

$x^{2}+\frac{4}{x+7}$

Final answer to the exercise

$x^{2}+\frac{4}{x+7}$

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