Question

(2x^3+16x^2-12x+9) ÷ (x+7)

Answer 1

`\bf 2x^3+16x^2-12x+9~~/~~ x+7\\\\ -------------------------------\\\\ x+7=0\implies x=\stackrel{our~divisor}{-7} \\\\\\ \begin{array}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+(191)/(x+7)}`

Answer 2

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