Question

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

Answer 1

Answer: C. $-x^3+x^2-1$

Step-by-step explanation:

Given Functions : $u(x) = x^5 - x^4 + x^2$

$v(x) = -x^2$

The expression equivalent to (u/v) (x) will be equivalent to $\dfrac{u(x)}{v(x)}$ , since polynomials allows division.

$\text{Now, }(u/v)(x)=\dfrac{u(x)}{v(x)}\\\\=\dfrac{x^5 - x^4 + x^2}{ -x^2}\\\\=\dfrac{x^5}{ -x^2}-\dfrac{x^4}{ -x^2}+\dfrac{x^2}{ -x^2}...........\text{Division law of exponents}\\\\=-x^{5-2}+x^{4-2}-x^{2-2}\\\\=-x^3+x^2-x^0\\\\=-x^3+x^2-1$

Hence, $(u/v)(x)=-x^3+x^2-1$

Answer 2

Hello,

Answer C if x≠0


(x^5-x^4+x²)/(-x²)=-x²(x^3-x²+1)/x²=-(x^3-x²+1)=-x^3+x²-1