Factor. Assume that variables used as exponents represent positive integers.

$$2 x^{2 n}+11 x^n+5$$

In March $2011$, the value of goods and services imported into the United States was $\$ 2.21 \times 10^{11}$. The estimated population was $3.11 \times 10^8$ people. Find the average value of imports per person in the United States for March $2011$. Round to the nearest dollar.

Perform the indicated operations.

$$\left(4 x^{2 a}-3 x^a+0.5\right)-\left(x^{2 a}-5 x^a-0.2\right)$$

Completely factor the polynomial.

$$x^4+8 x^2-20$$

Multiply. Assume that variables represent positive integers.

$$\left(x^a+y^{2 b}\right)\left(x^a-y^{2 b}\right)$$

Solve.

Write a sentence explain the meaning of the positive solution of Exercise 103.

Factor. Assume that variables used as exponents represent positive integers.

$$x^{3 n} \div 7 x^{11}-18$$

The estimated population of China at the end of $2010$ was $1.34 \times 10^9$ people. The land area of China is $3.705 \times 10^6$ square miles. Find the population density (number of people per square mile) for China at the end of $2010$. Round to the nearest whole.

In your own words, describe how to Find the degree of a polynomial.

Write the number in scientific notation.

$$36,800,000$$

With new plug-in hybrid autos and electric autos, it is very difficult to predict future sales of hybrids. One forecast is the equation $y=3 x^2-25 x+345$, where $x$ is the number of years past $2007$ and $y$ is the number of hybrid sales in thousands. Use this equation for this exercise.

Write a sentence explaining the meaning of the larger solution of the previous exercise.

Factor. Assume that variables used as exponents represent positive integers.

$$x^{2 n}-3 x^n-18$$

Solve.

Let $y=38.8$ and solve the resulting quadratic equation by factoring. (Hint When factoring, first factor out a factor of $0.7$ from all three terms of the trinomial.)

Completely factor the polynomial.

$$x^4-6 x^2-16$$