Question 1

Which of the following is the correct way to express $$\displaystyle \frac{3x$$^{-2}$$y^3$$}{$$6x^4y$$^{-1}$$}$$ using only positive exponents?

Accepted Answer

$$\displaystyle \frac{y^4$}{2x^6$}$$

Question 2

A biologist records the mass of a bacterium as $$0.00000032$$ grams. What is this number in scientific notation?

Accepted Answer

$$3.2 	imes 10$$^{-7}$$

Question 3

Simplify the expression $$\displaystyle (2x^3$y^2)^2$ \cdot (3x^2$y)^3$.

Accepted Answer

$$108x^{12}y^7$

Question 4

Which of the following is the degree of the polynomial $$5x^4y^2$ - 3x^2$y^5 + 7$?

Accepted Answer

$$7$$

Question 5

A chemist needs to multiply $$4.2 	imes 10^5$ by 3.0$$ 	imes $$10^{-3}$$ and express the answer in scientific notation. What is the result?

Accepted Answer

$$1.26 	imes 10$$^{2}$$

Question 6

Which of the following is a factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 7

Given the polynomial $$2x^3$$ - $$5x^2 + 4x - 7$, what is the coefficient of the x^2$ term?

Accepted Answer

$$-5$$

Question 8

A physics problem involves dividing $$6.0 	imes 10^8$ by 2.0$$ 	imes $$10^4. $$What is the answer in scientific notation?

Accepted Answer

$$3.0 	imes 10^4$

Question 9

Which of the following is the result of $$(x^2 + 2x + 1$$) - $$(x^2 - x + 3$$)$$?

Accepted Answer

$$3x - 2$$

Question 10

A rectangular garden has a length of $$(2x + 3)$$ meters and a width of $$(x - 2)$$ meters. What is the area of the garden, expressed as a polynomial?

Accepted Answer

$$2x^2 - x - 6$

Question 11

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 12

If $$f(x) = x^2$ - 4x + 3$$ and $$g(x) = 2x - 5$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$x^2 - 2x - 2$

Question 13

Which of the following is the result of multiplying $$(x + 2) by$$ $$(x - 5)$$?

Accepted Answer

$$x^2 - 3x - 10$

Question 14

A quadratic equation $$x^2 - 6x + 9 = 0$ models the height of a ball thrown upward. What are the solutions for x$?

Accepted Answer

$$x = 3 ($$double root)

Question 15

Which of the following is the result of dividing $$x^3$$ + $$2x^2 - x - 2$ by x + 2$?

Accepted Answer

$$x^2 + 2x - 1$

Question 16

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x - 5)(x + 3)$$

Question 17

A right triangle has legs of length $$x$$ and $$x + 2. $$According to the Pythagorean Theorem, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{x^2$ + (x + 2)^2$}$$

Question 18

Which of the following is the sum of $$3x^2 - 2x + 5$ and -x^2$ + 4x - 3$$?

Accepted Answer

$$2x^2 + 2x + 2$

Question 19

Which of the following is the correct factorization of $$4x^2 - 25$?

Accepted Answer

$$(2x - 5)(2x + 5)$$

Question 20

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). For what value of $$x is $$the profit maximized?

Accepted Answer

$$x = 2$$

Study Guide: Exponents, Polynomials, and Factoring (Chapters 4 and 5)

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