11 Mid-Chapter Quiz

Do you know HOW?

Simplify each expression. State any excluded values.

1. 6 x 2 − 24 x + 2 fraction 6 , x squared , minus 24 , over x plus 2 end fraction
2. 3 c + 9 3 c − 9 fraction 3 c plus 9 , over 3 c minus 9 end fraction
3. k − 2 k 2 + 2 k − 8 fraction k minus 2 , over k squared , plus 2 k minus 8 end fraction
4. 2 x 2 + 13 x + 15 2 x + 10 fraction 2 , x squared , plus 13 x plus 15 , over 2 x plus 10 end fraction
5. 9 − x 2 x 2 + x − 12 fraction 9 minus , x squared , over x squared , plus x minus 12 end fraction
6. Geometry The height of a rectangular prism is 3 more than twice its width w. The volume of the prism is 2 w 3 + 7 w 2 + 6 w . 2 , w cubed , plus 7 , w squared , plus 6 w .  Write a simplified expression for the length of the prism.

Multiply or divide.

7. 4 y 3 ⋅ − 3 5 y fraction 4 , over y cubed end fraction , dot . fraction negative 3 , over 5 y end fraction
8. z − 3 3 z ⋅ z + 8 z + 2 fraction z minus 3 , over 3 z end fraction . dot . fraction z plus 8 , over z plus 2 end fraction
9. x 2 − 4 x + 3 ⋅ x 2 + 7 x + 12 x − 2 fraction x squared , minus 4 , over x plus 3 end fraction . dot . fraction x squared , plus 7 x plus 12 , over x minus 2 end fraction
10. z + 5 z ÷ 3 z + 15 4 z fraction z plus 5 , over z end fraction . divides . fraction 3 z plus 15 , over 4 z end fraction
11. 2 a − 1 a − 3 ÷ ( a 2 − a − 6 ) fraction 2 eh minus 1 , over eh minus 3 end fraction . divides . open . eh squared , minus eh minus 6 . close
12. 4 d 2 − 3 d 7 d ÷ ( 4 d 2 + d − 3 ) fraction 4 , d squared , minus 3 d , over 7 d end fraction . divides . open . 4 , d squared , plus d minus 3 . close
13. ( 6 x 3 − 4 x 2 + 2 x ) ÷ 4 x 2 open 6 , x cubed , minus 4 , x squared , plus 2 x close divides 4 , x squared
14. What is the simplified form of 1 x + 5 3 x x 2 − 25 ? fraction fraction 1 , over x plus 5 end fraction , over fraction 3 x , over x squared , minus 25 end fraction end fraction . question mark
15. The length of a rectangle is 4 x + 1 4 x plus 1  and the area is 12 x 3 + 23 x 2 + 13 x + 2 . 12 , x cubed , plus 23 , x squared , plus 13 x plus 2 .  What is an expression for the width?

Add or subtract.

16. 3 8 x + 5 8 x fraction 3 , over 8 x end fraction , plus , fraction 5 , over 8 x end fraction
17. 5 y y + 3 − 7 y y + 3 fraction 5 y , over y plus 3 end fraction . minus . fraction 7 y , over y plus 3 end fraction
18. 3 5 x 2 + 5 2 x fraction 3 , over 5 , x squared end fraction . plus , fraction 5 , over 2 x end fraction
19. 4 t − 3 − 1 t − 2 fraction 4 , over t minus 3 end fraction . minus . fraction 1 , over t minus 2 end fraction
20. 2 x x − 5 + 9 x + 4 fraction 2 x , over x minus 5 end fraction . plus . fraction 9 , over x plus 4 end fraction

Do you UNDERSTAND?

21. Reasoning The expression p x 2 + x − 12 fraction p , over x squared , plus x minus 12 end fraction  simplifies to x + 5 x − 3 . fraction x plus 5 , over x minus 3 end fraction . .  Write the expression p represents.
22. Error Analysis Your friend says that the first step in simplifying x − 3 x + 4 ⋅ x 3 − x fraction x minus 3 , over x plus 4 end fraction . dot . fraction x , over 3 minus x end fraction  is to divide out the common factors x − 3 x minus 3  and 3 − x . 3 minus x .
    1. Explain your friend's error.
    2. What is a possible correct first step?
23. Writing A student's first step in finding the product 7 x · x 3 7 over x , middle dot , x cubed  was to rewrite the expression as 7 x ⋅ x 3 1 . 7 over x , dot , fraction x cubed , over 1 end fraction . .  Why do you think the student did this?
24. Compare and Contrast When you are dividing a polynomial by a monomial, you can multiply by the reciprocal or use long division. How are these two methods the same? How are they different? Which method do you prefer? Explain your answer.
25. Reasoning You are dividing a polynomial in one variable with a degree of 5 by a monomial in the same variable with a degree of 2. Would you expect the quotient to have a degree greater than or less than 5? Explain your answer.

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