Question

Look at the work shown for the division problem shown on the right. The remainder is 8 . Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2. f (–2) = 8 Compare the values you entered above. f (–2) is the remainder when dividing the polynomial by x + 2. Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.

Answer 1

To divide the polynomial 2x^4 - 4x^3 - 11x^2 + 3x - 6 by x + 2, we can use long division.

Step-by-step explanation:

To divide the polynomial 2x^4 - 4x^3 - 11x^2 + 3x - 6 by x + 2, we can use long division. Here are the steps:

1. Start by dividing the first term of the polynomial by the first term of the divisor. 2x^4 / x = 2x^3
2. Multiply the divisor, x + 2, by the quotient obtained in the previous step, 2x^3. 2x^3 * (x + 2) = 2x^4 + 4x^3
3. Subtract the result from the above step from the original polynomial: (2x^4 - 4x^3 - 11x^2 + 3x - 6) - (2x^4 + 4x^3) = -11x^2 + 3x - 6
4. Repeat the process with the new polynomial and continue until there are no more terms to divide.

Thus, the division of 2x^4 - 4x^3 - 11x^2 + 3x - 6 by x + 2 results in a quotient and a remainder.

Answer 2

1st : 8

2nd: 8

3rd: equal to