**5u^4 + 16u^3 - 15u^2 + 8u + 16 / u + 4 **

**Solution** **= 5u^3 - 4u^2 + u + 4**

Steps:

5u^4 + 16u^3 - 15u^2 + 8u + 16 / u + 4

Use the rational Root Theorem:

a/o = 16

a/n = 5

The dividers of a/o: 1, 16, 2, 4, 8

The dividers of a/n: 1, 5

Therefore check the following Rational Numbers:

+/- 1, 16, 2, 4, 8 / 1, 5

- 4 / 1 is a root of thye expression, So Factor out u + 4:

Compute:

5u^4 + 16u^3 - 15u^2 + 8u + 16 / u + 4, to get the rest of the equation: 5u^3 - 4u^2 + u + 4 = ( u + 4) (5u^3 - 4u^2 + u + 4 ) / u + 4

Cancel the Common Fact, you answer u + 4:

Hence, your answer is, 5u^3 - 4u^2 + u + 4

Hope that helps!!!!! : )