Answer:
2x^2 + x + 9 + (18/(x+2))
Explanation:
To find the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 using the long division method, you can follow these steps:
Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.
Multiply the divisor (x + 2) by 2x^2. The result is 2x^3 + 4x^2.
Subtract this result from the dividend (2x^3 - 5x^2 - 9x + 18). The result is -x^2 - 9x + 18
Bring down the next term of the dividend (-5x^2) and add it to the result from step 3. The result is -6x^2 - 9x + 18
Divide -6x^2 by -6x and the result is x.
Multiply the divisor by x. The result is x^2 + 2x
Subtract this result from the result of step 4. The result is -9x + 18
Bring down the next term of the dividend (-9x) and add it to the result from step 7. The result is -18x + 18
Divide -18x by -18 and the result is x
Multiply the divisor by x. The result is x^2 + 2x
Subtract this result from the result of step 8. The result is 18
Therefore, the quotient is 2x^2 + x + 9 and the remainder is 18
So the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 is 2x^2 + x + 9 + (18/(x+2))