Divide –3x3 – 4x2 + 4x +3 by x – 2.
work out
To divide -3x^3 - 4x^2 + 4x + 3 by x - 2, we can use long division.
-3x^2 - 2x + 8
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x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^3 divided by x is -3x^2.
Multiply -3x^2 by x-2 to get -3x^3 + 6x^2 and subtract it from the original expression to get:
-3x^3 - 4x^2 + 4x + 3
- (-3x^3 - 6x^2)
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2x^2 + 4x + 3
2x^2 divided by x is 2x.
Multiply 2x by x-2 to get 2x^2 - 4x and subtract it from the previous expression to get:
2x^2 + 4x + 3
- (2x^2 - 4x)
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8x + 3
8x divided by x is 8.
Multiply 8 by x-2 to get 8x - 16 and subtract it from the previous expression to get:
8x + 3
- (8x - 16)
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19
Since there are no more terms to divide, the remainder is 19.
Therefore, the quotient is -3x^2 - 2x + 8 and the remainder is 19.