Verified Answer :

Answer:

\(\Bigg(\displaystyle\frac{u}{v}\Bigg)(x) = -x^3 + x^2-1\)

Step-by-step explanation:

We are given the following in the question:

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

We have to find the expression for:

\(\Bigg(\displaystyle\frac{u}{v}\Bigg)(x) = \frac{u(x)}{v(x)}\\\\= \frac{x^5 - x^4 + x^2}{-x^2} = -\frac{x^5}{x^2} + \frac{x^4}{x^2} - \frac{x^2}{x^2}\\\\= -x^3 + x^2-1\)

We used the property of exponents to preform this division:

\(\displaystyle\frac{a^m}{a^n} = a^{m-n}\)

ashishdwivedilVT

The expression is equivalent to (U / V) (x) is -x³ + x² - 1.

What is Algebraic Division?

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Here, u(x) = x⁵ - x⁴ + x²

         v(x) = -x²

Now, on dividing u(x) by v(x), we get,

(u/v)(x) = \(\frac{x^5 - x^4 + x^2}{-x^2}\)

\(\frac{u}{v}(x) = \frac{x^5}{-x^2} - \frac{x^4}{-x^2}+\frac{x^2}{-x^2}\)

(u/v)(x) = -x³ + x² - 1

Thus, the expression is equivalent to (U / V) (x) is -x³ + x² - 1.

Learn more about Algebraic Division from:

https://brainly.com/question/16938364

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