divide -3x^(3)-4x^(2)+4x+3 by x-2

Answer 1

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.