Question

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

Answer 1

Option c is the correct answer. (u/v)(x) = (-x³ + x² - 1) is the answer.

Explanation:

We have two expressions:

u(x) = x⁵ - x⁴ +x²

v(x) = -x²

we have to find (u/v)(x).

For this we have to divide these functions.

(u/v)(x) = ( x⁵ - x⁴ +x²) /( -x² )

Taking -x² common from nominator.

(u/v)(x) = -x²(-x³ + x² - 1) / ( -x²)

Simplify the equation.

(u/v)(x) = (-x³ + x² - 1)

So, option c is the correct answer.

Answer 2

c) -x^3 + x^2 - 1

Explanation:

Given: u (x) = x^5 - x^4 +x^2 and v(x) = -x^2

(u/v)(x) = u(x)/v(x)

Now plug in the given functions in the above formula, we get

= (x^5 - x^4 + x^2) / -x^2

We can factorize the numerator.

In x^5 - x^4 + x^2. the common factor is x^2, so we can take it out and write the remaining terms in the parenthesis.

= x^2 (x^3 - x^2 + 1) / - x^2

Now we gave x^2 both in the numerator and in the denominator, we can cancel it out.

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

When we dividing the numerator by -1, we get

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

Answer: c) -x^3 + x^2 - 1

Hope you will understand the concept.

Thank you.