SOLUTION: how do you divide problems with variables. Such as (4x^3-3x^2+7x-19)/x-2 i've tried looking in my text book but they don't show what to do when their is addition of the denom

Question 536766: how do you divide problems with variables.
Such as
(4x^3-3x^2+7x-19)/x-2
i've tried looking in my text book but they don't show what to do when their is addition of the denominator.
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
Do it like long division.

Look at x-2 into 4x^3-3x^2+7x-19.

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.

x^2 * (x-2) = x^3 - 2x^2.

4x^3 - 3x^2 - (x^3 - 2x^2)=3x^3 - x^2.

X^2 is the first part of the answer. Carry down the next term which is 7x

Now look at 3x^3 -x^2 +7x.

What can multiply x-2 to go into that? -x.

-x *(x-2) = -x^2 + 2x

3x^3 -x^2 +7x -(-x^2 + 2x) = 3x^3 + 5x

The answer so far is x^2 - x.

Carry down the -19. That makes it.

3x^3 + 5x - 19.

x-2 goes into that 5 times.

5(x-2)= 5x - 10.

3x^3 + 5x - 19 - (5x - 10) = 3x^3 - 9.

Remember, in long division the divisor goes over the remainder as the fractional part of a mixed number.

The quotient (result of this division) is:

That can be simplified to:

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