divide -3x^(3)-4x^(2)+4x+3 by x-2
To perform polynomial long division, we first set up the division as follows:
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x - 2 | -3x^3 - 4x^2 + 4x + 3
Now, we divide the highest degree term of the dividend (-3x^3) by the highest degree term of the divisor (x):
-3x^3 / x = -3x^2
Next, we multiply the divisor (x - 2) by the quotient (-3x^2):
(x - 2) * (-3x^2) = -3x^3 + 6x^2
Now, we subtract the result (-3x^3 + 6x^2) from the dividend:
-3x^3 - 4x^2 + 4x + 3 - (-3x^3 + 6x^2) = -10x^2 + 4x + 3
Now, we bring down the next term of the dividend (-10x^2) and repeat the process:
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x - 2 | -3x^3 - 4x^2 + 4x + 3
- (-10x^2)
We divide -10x^2 by x to get -10x:
-10x^2 / x = -10x
Multiply the divisor (x - 2) by the quotient (-10x):
(x - 2) * (-10x) = -10x^2 + 20x
Subtract the result (-10x^2 + 20x):
-10x^2 + 20x - (-10x^2 + 20x) = 0
Since the result is 0, we have divided completely. Therefore, the final quotient is:
-3x^2 - 10x
So, the division of -3x^3 - 4x^2 + 4x + 3 by x - 2 is equal to -3x^2 - 10x.