Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3

To find the remainder when a polynomial is divided by another polynomial, we can use the polynomial long division method. The steps for polynomial long division are as follows: 1. Divide the highest degree term of the dividend (2x^3 in this case) by the highest degree term of the divisor (x+3) and write the result above the long division bracket. 2. Multiply the divisor (x+3) by the quotient obtained in step 1 and write the result below the dividend. 3. Subtract the result obtained in step 2 from the dividend and write the remainder below. 4. Bring down the next term of the dividend and repeat steps 1-3 until there are no more terms to bring down. Using this method, we can divide 2x^3 - 11x^2 + 8x - 1 by x + 3 to find the remainder: 2x^2 - 17x + 51 ______________________ x + 3 | 2x^3 - 11x^2 + 8x - 1 2x^3 + 6x^2 ____________ -17x^2 + 8x -17x^2 - 51x ____________ 59x - 1 59x + 177 ________ -178 Therefore, the remainder when 2x^3 - 11x^2 + 8x - 1 is divided by x + 3 is -178.