Question 1206090
{{{(-2x^3 + 5x^2 - x + 2) /(x + 2)}}}

using long division

...........({{{-2x^2+9x-19}}}
{{{(x + 2)}}}|{{{-2x^3 + 5x^2 - x + 2}}}
............{{{-2x^3-4x^2}}}............subtract
......................{{{9x^2}}}...........bring {{{-x}}} down
......................{{{9x^2-x}}}
......................{{{9x^2+18x}}}...........subtract
...............................{{{-19x}}}..........bring {{{2}}} down
...............................{{{-19x+2}}}
...............................{{{-19x-38}}}..........subtract
.......................................{{{40}}} => reminder


{{{-2 x^3 + 5 x^2 - x + 2 = (-2 x^2 + 9 x - 19)(x + 2) + 40}}}


verify solution by using synthetic division

Write the coefficients of the dividend to the right.

.....|{{{x^3}}}|{{{x^2}}}|{{{x^1}}}|{{{x^0}}}
{{{-2}}}|...{{{-2}}}|...{{{5}}}|...{{{-1}}}|...{{{2}}}|


Write down the first coefficient without changes:

<a href="https://ibb.co/NKbj3B8"><img src="https://i.ibb.co/NKbj3B8/Capture2-13-2024-5-54-18-PM.jpg" alt="Capture2-13-2024-5-54-18-PM" border="0"></a>


<a href="https://ibb.co/xjkHXYt"><img src="https://i.ibb.co/xjkHXYt/Capture2-13-2024-5-56-37-PM.jpg" alt="Capture2-13-2024-5-56-37-PM" border="0"></a>

<a href="https://ibb.co/rsqYNXF"><img src="https://i.ibb.co/rsqYNXF/Capture2-13-2024-5-58-30-PM.jpg" alt="Capture2-13-2024-5-58-30-PM" border="0"></a>


We have obtained the following resulting coefficients:

 {{{-2}}},{{{9}}},{{{-19}}},{{{40}}} (the last coefficient is the remainder)

 the quotient is {{{-2x^2+9x-19}}}, and the remainder is {{{40}}}