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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.This module contains the proficiency exam for the chapter "Algebraic Expressions and Equations".

Proficiency exam

( [link] ) In the expression below, specify the number of terms that are present, then list them.
3 a ( a + 1 ) ( a + 2 ) ( a 3 )

two: 3 a ( a + 1 ) , ( a + 2 ) ( a 3 )

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( [link] ) List, if there are any, the common factors of
20 x 3 y 2 + 15 x 3 y 2 z 2 + 10 x 3 z 2

5 x 3

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( [link] ) How many y 2 ( b + 2 ) ' s in 8 x y 2 ( b + 2 ) ( b 6 ) ?

8 x ( b 6 )

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( [link] ) Write the coefficient of x 3 in 8 x 3 y 3 z .

8 y 3 z

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( [link] ) Find the value of P 2 if k = 4 and a = 3 .
P 2 = k a 3

108

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( [link] ) Classify the polynomial given below as a monomial, binomial, trinomial, or none of these. Specify the degree of the polynomial and write the numerical coefficient of each term.
3 x 3 y + 4 x y 4 + 8 x 2 y 2 z 0 w , z 0

trinomial; 5th degree;
numberical coefficients: 3, 4, 8

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Simplify the algebraic expressions for the following problems.

( [link] ) 4 x 2 + 3 x + 2 x + 11 x 2 3

15 x 2 + 5 x 3

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( [link] ) 3 a [ 2 ( a + 1 ) + 4 ] 18 a

6 a 2

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( [link] ) ( x + 2 ) ( x + 4 )

x 2 + 6 x + 8

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( [link] ) ( 3 a 7 ) ( 2 a + 10 )

6 a 2 + 16 a 70

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( [link] ) ( y + 3 ) 2

y 2 + 6 y + 9

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( [link] ) ( 6 a + 7 y ) 2

36 a 2 + 84 a y + 49 y 2

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( [link] ) ( 4 x 9 y ) 2

16 x 2 72 x y + 81 y 2

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( [link] - [link] ) 3 x 2 ( 2 x + 5 ) ( 3 x + 1 )

18 x 4 + 51 x 3 + 15 x 2

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( [link] - [link] ) ( 3 a b ) ( 4 a 3 b )

12 a 2 13 a b + 3 b 2

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( [link] - [link] ) 6 y 2 ( 2 y + 3 y 2 4 )

18 y 4 12 y 3 + 24 y 2

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( [link] - [link] ) 4 b 3 ( b 2 1 ) 2

4 b 7 + 8 b 5 4 b 3

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( [link] - [link] ) ( 2 a 3 + 3 b 2 ) 2

4 a 6 + 12 a 3 b 2 + 9 b 4

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( [link] - [link] ) 6 a ( a 2 ) ( 2 a 2 + a 11 )

4 a 2 13 a + 11

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( [link] - [link] ) ( 5 h + 2 k ) ( 5 h 2 k )

25 h 2 4 k 2

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( [link] - [link] ) Subtract 4 a 2 10 from 2 a 2 + 6 a + 1 .

2 a 2 + 6 a + 11

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( [link] - [link] ) Add three times 6 x 1 to two times 4 x + 5 .

10 x + 7

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( [link] - [link] ) Evaluate 6 k 2 + 2 k 7 if k = 1 .

3

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( [link] - [link] ) Evaluate 2 m ( m 3 ) 2 if m = 4 .

392

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( [link] ) What is the domain of y = 3 x 7 x + 3 ?

all real numbers except  ( 3 )

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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