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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