Question

Find the quotient and remainder (x⁴ -3x³+18x+1)/(x+2)

Answer 1

To find the quotient and remainder of the polynomial division (x⁴ - 3x³ + 18x + 1)/(x + 2), we can use polynomial long division. The quotient is x³ - 5x² + 10x - 19 and the remainder is 39.

Step-by-step explanation:

To find the quotient and remainder of the polynomial division (x⁴ - 3x³ + 18x + 1)/(x + 2), we can use polynomial long division.

1. Divide the first term of the numerator, x⁴, by the first term of the denominator, x, to get x³ as the first term of the quotient.
2. Multiply the entire denominator, x + 2, by x³ to get x⁴ + 2x³. Subtract this from the numerator.
3. Bring down the next term of the numerator, -3x³.
4. Repeat the process above with the new numerator, -3x³ + 2x⁴ (after subtracting).
5. Continue until all terms of the numerator have been divided.

The quotient is x³ - 5x² + 10x - 19 and the remainder is 39.