Question

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

a) x3 – x2
b)–x3 + x2
c)–x3 + x2 – 1
d)x3 – x2 + 1

Answer 1

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

Answer 2

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

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
`(u(x))/(v(x))` , since polynomials allows division.

`\text{Now, }(u/v)(x)=(u(x))/(v(x))\\\\=(x^5 - x^4 + x^2)/( -x^2)\\\\=(x^5)/( -x^2)-(x^4)/( -x^2)+(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`