Question

If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (U divided by V) (x)

Answer 1

To find the equivalent of the equations U divided by V where as u(x) = x^5 - x^4 + x^2 and v(x) = -x^2, first you have to factor out the U first and came up with (x^2)(x^3-x^2+1) then divide it by -x^2 which cancel the X^2 and the answer would become -(x^3-X^2+1), i hope you are satisfied with my answer

Answer 2

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:

$\displaystyle\frac{a^m}{a^n} = a^{m-n}$