<PRE><B>Question 536766</B>
Do it like long division.&lt;P&gt;
Look at x-2 into 4x^3-3x^2+7x-19.&lt;P&gt;
Does x-2 go into 4x^3 and 3x^2 by multiplying x-2 by the same number?  Yes, if the number is x^2.&lt;P&gt;
x^2 * (x-2) = x^3 - 2x^2.&lt;P&gt;
4x^3 - 3x^2 - (x^3 - 2x^2)=3x^3 - x^2.&lt;P&gt;
X^2 is the first part of the answer.  Carry down the next term which is 7x&lt;P&gt;
Now look at 3x^3 -x^2 +7x.  &lt;P&gt;
What can multiply x-2 to go into that?  -x.&lt;P&gt;
-x *(x-2) = -x^2 + 2x &lt;P&gt;
3x^3 -x^2 +7x -(-x^2 + 2x) = 3x^3  + 5x&lt;P&gt;
The answer so far is x^2 - x.&lt;P&gt;
Carry down the -19.  That makes it.&lt;P&gt;
3x^3 + 5x - 19.&lt;P&gt;
x-2 goes into that 5 times.&lt;P&gt;
5(x-2)= 5x - 10.&lt;P&gt;
3x^3 + 5x - 19 - (5x - 10) = 3x^3 - 9.&lt;P&gt;
Remember, in long division the divisor goes over the remainder as the fractional part of a mixed number.&lt;P&gt;
The quotient (result of this division) is:&lt;P&gt;
{{{(x^2 - x + 5) + (3x^3 - 9)/(x-2)}}}&lt;P&gt;
That can be simplified to:&lt;P&gt;
{{{(x^2 - x + 5) + (3(x^3 - 3))/(x-2)}}}
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