Question

If u(x) = x^5 - x^4 + x^2 and v (x) = -x^2 which expression is equivalent to ( u/ v) (x)

Answer 1

(u/v)(x) = -x³+x²-1

Explanation:

We have given two functions.

u(x) = x⁵ - x⁴ + x² and v (x) = -x²

We have to find the quotient of the given two functions.

(u/v)(x) = ?

The formula to find the quotient is:

(u/v)(x) = u(x) / v(x)

Putting given values in above formula, we have

(u/v)(x) = x⁵-x⁴+x² / -x²

(u/v)(x) = -x²(-x³+x²-1) / -x²

(u/v)(x) = -x³+x²-1 which is the answer.

Answer 2

`(u/v)(x)=-x^(3)+x^(2)-1`

Explanation:

You have the following functions:

`u(x)=x^(5)-x^(4)+x^(2)\\v(x)=-x^(2)`

Therefore
`(u/v)(x)` indicates that you must divide both functions, as you can see below:

`(u/v)(x)=(x^(5)-x^(4)+x^(2))/(-x^(2))`

Simplify it. Therefore, you obtain:

`(u/v)(x)=(x^(5)-x^(4)+x^(2))/(-x^(2))\\\\(u/v)(x)=-x^(3)+x^(2)-1`