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

Simplify.

$$3 \sqrt{5 b}-4 \sqrt{5 b}+11 \sqrt{5 b}$$

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

Write the following fractions as decimals in hundredths with the remainder expressed as a fra ction.

$$\dfrac{1}{6}$$

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

$$f(x) = 3x^5-4x^3+x+5 ; \quad p(x) = x^3-2x+7$$

Does the quotient of 4554 ÷ 9 have a remainder? How can you tell without dividing?

Add or subtract.

$$\frac{5}{c-5}+\frac{9}{c-5}$$

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

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.

Simplify the remaining expression completely.

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

Find the quotient and the remainder.

$$\frac { 1 - 2 x + 3 x ^ { 2 } - 4 x ^ { 3 } } { x - 2 }$$

Solve the system.

$$2(5 a-5 b)=10$$

$$-5(6 a+2 b)=10$$

a. The table below shows the fraction A of the original area of a piece of paper that remains after the paper has been cut in half n times. Graph the function represented by the table. Is the function linear or nonlinear? Cutting Paper

$$\begin{matrix} \text{Number of Cuts, n} & \text{1} & \text{2} & \text{3} & \text{4}\\ \text{Fraction of Original Area Remaining, A} & \ {\frac{1}{2}} & \ {\frac{1}{4}} & \ {\frac{1}{8}} & \ {\frac{1}{16}}\\ \end{matrix}$$

b. Will the area A in part (a) ever reach zero? Explain.

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

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