Answer:
[tex]\Bigg(\displaystyle\frac{u}{v}\Bigg)(x) = -x^3 + x^2-1[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]u(x) = x^5 - x^4 + x^2\\v(x) = -x^2[/tex]
We have to find the expression for:
[tex]\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[/tex]
We used the property of exponents to preform this division:
[tex]\displaystyle\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression is equivalent to (U / V) (x) is -x³ + x² - 1.
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) = [tex]\frac{x^5 - x^4 + x^2}{-x^2}[/tex]
[tex]\frac{u}{v}(x) = \frac{x^5}{-x^2} - \frac{x^4}{-x^2}+\frac{x^2}{-x^2}[/tex]
(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:
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