x^3+4x^2+6x-4=

To solve this problem, we can use polynomial long division.

First, we divide the first term of the numerator, x^3, by the numerator of the denominator, x:

x^3 / x = x^2

Next, we multiply x-4 by x^2 to get x^3 - 4x^2. We subtract this from the numerator:

(x^3 + 4x^2 + 6) - (x^3 - 4x^2) = 8x^2 + 6

Now we repeat the process with the new numerator, 8x^2 + 6, and the denominator, x-4:

8x^2 / x = 8x

Multiply x-4 by 8x to get 8x^2 - 32x. Subtract this from the numerator:

(8x^2 + 6) - (8x^2 - 32x) = 32x + 6

Finally, we repeat the process with the new numerator, 32x + 6, and the denominator, x-4:

32x / x = 32

Multiply x-4 by 32 to get 32x - 128. Subtract this from the numerator:

(32x + 6) - (32x - 128) = 134

Therefore, (x^3+4x^2+6)/(x-4) = x^2 + 8x + 32 with a remainder of 134