Question

(2x^3+16x^2-12x+9) ÷ (x+7)

Answer 1

Always eliminate the first one before moving on. Remember to drop down monomials, like you would a normal division problem.

                     2x² + 10x + 18
         __________________
x + 3 | 2x³ + 16x² - 12x + 9
         -(2x³ + 6x²)
         -------------------------------
                    10x² - 12x
                  -(10x² - 30x)
         -----------------------------
                            + 18x + 9
                          - (18x + 54)
                    ----------------------
                                      -45


  2x² + 10x + 18        R: -45/x + 3 is your answer R: = remainder


hope this helps

Answer 2

$\bf 2x^3+16x^2-12x+9~~\div~~ x+7\\\\ -------------------------------\\\\ x+7=0\implies x=\stackrel{our~divisor}{-7} \\\\\\ \begin{array}{r|rrrrrr} -7&&2&16&-12&9\\ &&&-14&-14&182\\ --&&--&--&--&--\\ &&2&2&-26&\boxed{191}&\leftarrow remainder \end{array} \\\\\\ \stackrel{quotient}{2x^2+2x-26}\qquad \qquad \qquad \qquad \stackrel{\textit{we can also write it like}}{2x^2+2x-26+\frac{191}{x+7}}$