Write the expression in the form

$$\text { quotient }+\frac{\text { remainder }}{\text { divisor }} \text {. }$$

$$\frac{3 x+1}{x}$$

Show that the results of parts (a) and (b) of as we discussed earlier remain true for subgroups $I, J$ of an abelian group A.

Suppose that

$$P ( x ) = x ^ { 100 } - x ^ { 99 } + x ^ { 98 } - x ^ { 97 } + \cdots + x ^ { 2 } - x + 1$$

. Find the remainder when P(x) is divided by x + 1.

Determine if $P(x)=3 x^3-4 x^2-28 x-16$ has a zero remainder when divided by $x+2$. Determine $Q(x)$.

Find the quotient and remainder. $\left(2 x^{3}+9 x^{2}+11 x+3\right) \div(2 x+3)$

Find the quotient q(x) and remainder r(x) when ƒ(x) is divided by g(x). ƒ(x) = 2x³ - 3x² + x - 1, g(x) = 3x³ + 4x - 5

Simplify each expression so that only positive exponents remain.

$$\frac{x^{1 / 3}}{x^{-2 / 3}}$$

Simplify the remaining expression completely.

$$\dfrac{x^6y^4}{xy^2}$$

Simplify. $-5 n\left(2 n^2\right)-(-5 n)(8 n)+(-5 n)(4)$

Determine the inverse of the linear function, where y=f(x).

$$y-y_1=m\left(x-x_1\right)$$

Find the quotient and remainder if $f(x)$ is divided by $p(x)$.

$$f(x) = 3 x^4+2 x^3-x^2-x-6 ; \quad p(x) = x^2+1$$

Which of the following is (are) rich source(s) of vitamin E?
a. raw vegetable oil
b. colorful foods, such as carrots
c. milk and milk products
d. raw cabbage

If $2 x+5=-5$ and $3 y+5=-10,$ find the value of $x^{3}-y^{3}$.

The classic Millikan oil drop experiment setup is shown in the given figure. In this experiment oil drops are suspended in a vertical electric field against the gravitational force to measure their charge. If the mass of a negatively charged drop suspended in an electric field of $1.18 \times 10^{-4} \mathrm{~N} / \mathrm{C}$ strength is $3.85 \times 10^{-21} \mathrm{~g}$, find the number of excess electrons in the drop.