Answer:
B. 2, 6, 0, 8; x^3 + 3x^2 - 4
Explanation:
When we divide x^4+x^3-6x^2-4x+8 by x-2, the synthetic division is equal to
Because the first 1 is moved down. Then, 1 x 2 = 2, so we type 2 under the next number and add, so 1 + 2 = 3
We continue with the same proccess, so 3 x 2 = 6 and -6 + 6 = 0
0 x 2 = 0 and -4 + 0 = -4
-4 x 2 = -8 and 8 - 8 = 0
Therefore, the missing numbers are 2, 6, 0 and -8 and the quotient is equal to
x^3 + 3x^2 + 0x - 4
x^3 + 3x^2 - 4
Because each number below the line is the coefficient of the powers of x in descendent order.
So, the answer is
B. 2, 6, 0, 8; x^3 + 3x^2 - 4
