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