Think you’ve got your head wrapped around Polynomial Division and Rational Expressions? Put your knowledge to
the test. Good luck — the Stickman is counting on you!
Q.
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_1.png)
evaluated at x = 4 is
0
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_2.png)
1
-2
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Q.
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_3.png)
evaluated at x = -3 is
0
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_4.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_5.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_6.png)
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Q. The constant 0 is
not a function.
neither a polynomial nor a rational expression.
a polynomial but not a rational expression.
a rational expression but not a polynomial.
both a polynomial and a rational expression.
Q. Which two expressions are equivalent to each other?
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_12.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_13.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_14.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_15.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_16.png)
Q. The expressions
are equivalent for:
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_17.png)
all values of x.
all values of x except 0 and -4.5.
all values of x except 3.5.
all values of x except 0, 3.5, and 4.5.
no values of x.
Q.
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_18.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_19.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_20.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_21.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_22.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_23.png)
Q. Find the quotient
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_25.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_26.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_27.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_28.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_29.png)
Q. Which of the following statements is not always true?
The sum of two rational expressions is a rational expression.
The sum of two rational expressions is never a rational expression.
The difference of two rational expressions is a rational expression.
The product of two rational expressions is a rational expression.
The quotient of two rational expressions is a rational expression.
Q. Which of the following is a valid simplification of the complex rational expression
?
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_31.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_32.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_33.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_34.png)
![](https://media1.shmoop.com/images/algebra/alg_polydiv_quiz2_latek_35.png)