Answer: C. [tex]-x^3+x^2-1[/tex]
Step-by-step explanation:
Given Functions : [tex]u(x) = x^5 - x^4 + x^2[/tex]
[tex]v(x) = -x^2[/tex]
The expression equivalent to (u/v) (x) will be equivalent to [tex]\dfrac{u(x)}{v(x)}[/tex] , since polynomials allows division.
[tex]\text{Now, }(u/v)(x)=\dfrac{u(x)}{v(x)}\\\\=\dfrac{x^5 - x^4 + x^2}{ -x^2}\\\\=\dfrac{x^5}{ -x^2}-\dfrac{x^4}{ -x^2}+\dfrac{x^2}{ -x^2}...........\text{Division law of exponents}\\\\=-x^{5-2}+x^{4-2}-x^{2-2}\\\\=-x^3+x^2-x^0\\\\=-x^3+x^2-1[/tex]
Hence, [tex](u/v)(x)=-x^3+x^2-1[/tex]
