Question 1

Simplify the expression $$\left( \dfrac{3}{2} x^5$ \right) \left( \dfrac{2}{3} x^3$ \right). $$What is the result?

Accepted Answer

$$x^8$$

Question 2

Which of the following is equivalent to $$\dfrac{3x^7$}{15x^5$}$$?

Accepted Answer

$$\dfrac{1}{5}x^2$

Question 3

Simplify $$\left( \dfrac{x^3$ y^4$}{x^6$ y^2$} \right). $$Which of the following is correct?

Accepted Answer

$$\dfrac{y^2$}{x^3$}$$

Question 4

Write $$\dfrac{2.0 	imes 10^4$ + 2.32 	imes 10^2$}{1.5 	imes 10^4$} in $$scientific notation, rounded to two significant digits.

Accepted Answer

$$1.4 	imes 10^0$

Question 5

Which of the following is an equivalent expression to $$\dfrac{y$$^{-2}$$}{p$$^{-3}$$ y$$^{-3}$$}$$ using only positive exponents?

Accepted Answer

$$\dfrac{p^3$ y}{1}$$

Question 6

A state has a population of $$1.2807060 	imes 10^7$ people. If each person drinks 6.25$$ 	imes $$10^3$$ ounces of soda per year, what is the total soda consumption in scientific notation?

Accepted Answer

$$8.0 	imes 10$$^{10}$$

Question 7

Simplify $$\dfrac{6.0 	imes 10^5$}{3.2 	imes 10$$^{-11}$$}$$ and write your answer in scientific notation, rounded to two significant digits.

Accepted Answer

$$1.9 	imes 10$$^{16}$$

Question 8

What is the degree of the term $$15m^5$$ $$n^3 p$?

Accepted Answer

$$9$$

Question 9

Evaluate $$\dfrac{x^2$ + 3x^6$}{x$$^{-1}$$}$$ for $$x = -1.$$

Accepted Answer

$$-4$$

Question 10

Given the polynomial $$-x^4$$ + $$12x^3$$ - $$5x^2 + 2x - 3$, which of the following is the leading coefficient?

Accepted Answer

$$-1$$

Question 11

A rectangular room is $$w$$ feet wide and $$(3w-2)$$ feet long. Which polynomial represents the perimeter of the room?

Accepted Answer

$$8w - 4$$

Question 12

Add the polynomials: $$(6x^2 - 3x + 4$$) + $$(5x^2 + x - 2$$)$$. What is the result?

Accepted Answer

$$11x^2 - 2x + 2$

Question 13

Subtract the polynomials: $$(5r^3$$ - $$2r^2 + 4r - 5$$) - $$(3r^2 - 5r + 4$$)$$. What is the result?

Accepted Answer

$$5r^3$$ - $$5r^2 + 9r - 9$

Question 14

Multiply: $$(2m + 1)(m - 5). $$What is the simplified result?

Accepted Answer

Question 15

Multiply: $$(2x + 1)(3x^2$ - 5x + 3). $$What is the simplified result?

Accepted Answer

$$6x^3$$ - $$7x^2 + x + 3$

Question 16

Simplify $$\dfrac{x^3$ y^5$}{x^4$ y^3$}. $$Which of the following is correct?

Accepted Answer

$$\dfrac{y^2$}{x}$$

Question 17

A moderately active woman’s daily caloric needs are estimated by $$917 + 6w + 6h - 6a$$, where $$w is $$weight in pounds, $$h is $$height in inches, and $$a is $$age in years. If Christine weighs 125 lb, is 64 in. tall, and is 27 years old, what are her daily caloric needs?

Accepted Answer

$$1,435$$

Question 18

Which of the following is the term of lowest degree in the polynomial $$-x^4$$ + $$12x^3$$ - $$5x^2 + 2x - 3$?

Accepted Answer

$$-3$$

Question 19

Multiply: $$(4x^2 - 2x$$ + $$7)(x^3$$)$$. What is the result?

Accepted Answer

$$4x^5$$ - $$2x^4$$ + $$7x^3$$

Unit 4 Review: Beginning & Intermediate Algebra Guidance

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