Exam 5: Exponents and Polynomials

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -Approximately 7 × 103 employees of a certain company average $30,000 each year in salary. What is the total amount earned by all the employees of this company per year?

Add or subtract. - $\left( x ^ { 3 } - 3 x ^ { 2 } + 20 x \right) - \left( 6 x ^ { 2 } - 6 x + 13 \right)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( x ^ { - 4 } y ^ { 6 } \right) ^ { - 1 }$

Evaluate the given function. - $f ( x ) = x ^ { 4 } , f \left( b ^ { 5 } \right)$

Divide. Assume all variables are nonzero. - $\frac { - 12 x ^ { 11 } - 16 x ^ { 7 } } { - 4 x ^ { 3 } }$

Divide. Assume all variables are nonzero. - $\frac { 27 x ^ { 4 } + 27 x } { 9 }$

Simplify. (Assume all variables are nonzero.) - $\frac { 4 } { 7 ^ { 0 } }$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The mass of an electron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of $813,000,000$ electrons.

Find the missing dividend or divisor. - $\frac { 36 x ^ { 3 } + 27 x ^ { 2 } + 72 x } { ? } = 4 x ^ { 2 } + 3 x + 8$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = x + 2 , g ( x ) = x + 4$

Find the missing polynomial. - $\left( 7 x ^ { 5 } - 4 x ^ { 2 } + 2 x \right) + ? = 16 x ^ { 5 } + 2 x ^ { 2 } - 3 x$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -The national debt of a small country is $\$ 7,370,000,000$ and the population is $2,662,000$ . What is the amount of debt per person?

Solve the problem. -The number of feet traveled by a free-falling object in t seconds is given by the function f(t) = 16t How far would it fall in 8 seconds?

Identify the polynomial as a monomial, binomial or trinomial. - $- 6 x ^ { 4 } - 6 x ^ { 3 } + 6$

Multiply. - $- 5 x ^ { 2 } z ^ { 4 } \cdot 4 x ^ { 3 } z ^ { 2 }$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $4 x ^ { 6 } - 9 x ^ { 7 } + 10 x ^ { 2 } - 7$

Identify the polynomial as a monomial, binomial or trinomial. - $11 x ^ { 5 } + 3 x - 4$

Find the missing monomial, factor or term. - $( x + 10 ) \cdot ? = x ^ { 2 } - 100$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $- 3 x ^ { 4 } - 13 x ^ { 2 } + 6 x + 4 x ^ { 6 }$

List the degree of each term and the degree of the polynomial. - $3 x ^ { 8 } y 8 - 3 x ^ { 2 } y ^ { 2 } + 8 x ^ { 3 } y$