Review Exercises

For the following exercises, perform the given operations.

( 5 − 3 ⋅ 2 ) 2 − 6 ( 5 − 3 ⋅ 2 ) 2 − 6

64 ÷ ( 2 ⋅ 8 ) + 14 ÷ 7 64 ÷ ( 2 ⋅ 8 ) + 14 ÷ 7

2 ⋅ 5 2 + 6 ÷ 2 2 ⋅ 5 2 + 6 ÷ 2

For the following exercises, solve the equation.

5 x + 9 = −11 5 x + 9 = −11

2 y + 4 2 = 64 2 y + 4 2 = 64

For the following exercises, simplify the expression.

9 ( y + 2 ) ÷ 3 ⋅ 2 + 1 9 ( y + 2 ) ÷ 3 ⋅ 2 + 1

3 m ( 4 + 7 ) − m 3 m ( 4 + 7 ) − m

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

Exponents and Scientific Notation

For the following exercises, simplify the expression.

2 2 ⋅ 2 4 2 2 ⋅ 2 4

4 5 4 3 4 5 4 3

( a 2 b 3 ) 4 ( a 2 b 3 ) 4

6 a 2 ⋅ a 0 2 a −4 6 a 2 ⋅ a 0 2 a −4

( x y ) 4 y 3 ⋅ 2 x 5 ( x y ) 4 y 3 ⋅ 2 x 5

4 −2 x 3 y −3 2 x 0 4 −2 x 3 y −3 2 x 0

( 2 x 2 y ) −2 ( 2 x 2 y ) −2

( 16 a 3 b 2 ) ( 4 a b −1 ) −2 ( 16 a 3 b 2 ) ( 4 a b −1 ) −2

Write the number in standard notation: 2.1314 × 10 −6 2.1314 × 10 −6

Write the number in scientific notation: 16,340,000

Radicals and Rational Expressions

For the following exercises, find the principal square root.

49 1250 49 1250

4 3 + 6 3 4 3 + 6 3

12 5 − 13 5 12 5 − 13 5

250 3 −8 3 250 3 −8 3

Polynomials

For the following exercises, perform the given operations and simplify.

( 3 x 3 + 2 x − 1 ) + ( 4 x 2 − 2 x + 7 ) ( 3 x 3 + 2 x − 1 ) + ( 4 x 2 − 2 x + 7 )

( 2 y + 1 ) − ( 2 y 2 − 2 y − 5 ) ( 2 y + 1 ) − ( 2 y 2 − 2 y − 5 )

( 2 x 2 + 3 x − 6 ) + ( 3 x 2 − 4 x + 9 ) ( 2 x 2 + 3 x − 6 ) + ( 3 x 2 − 4 x + 9 )

( 6 a 2 + 3 a + 10 ) − ( 6 a 2 −3 a + 5 ) ( 6 a 2 + 3 a + 10 ) − ( 6 a 2 −3 a + 5 )

( k + 3 ) ( k − 6 ) ( k + 3 ) ( k − 6 )

( 2 h + 1 ) ( 3 h − 2 ) ( 2 h + 1 ) ( 3 h − 2 )

( x + 1 ) ( x 2 + 1 ) ( x + 1 ) ( x 2 + 1 )

( m − 2 ) ( m 2 + 2 m − 3 ) ( m − 2 ) ( m 2 + 2 m − 3 )

( a + 2 b ) ( 3 a − b ) ( a + 2 b ) ( 3 a − b )

( x + y ) ( x − y ) ( x + y ) ( x − y )

Factoring Polynomials

For the following exercises, find the greatest common factor.

81 p + 9 p q − 27 p 2 q 2 81 p + 9 p q − 27 p 2 q 2

12 x 2 y + 4 x y 2 −18 x y 12 x 2 y + 4 x y 2 −18 x y

88 a 3 b + 4 a 2 b − 144 a 2 88 a 3 b + 4 a 2 b − 144 a 2

For the following exercises, factor the polynomial.

2 x 2 − 9 x − 18 2 x 2 − 9 x − 18

8 a 2 + 30 a − 27 8 a 2 + 30 a − 27

d 2 − 5 d − 66 d 2 − 5 d − 66

x 2 + 10 x + 25 x 2 + 10 x + 25

y 2 − 6 y + 9 y 2 − 6 y + 9

4 h 2 − 12 h k + 9 k 2 4 h 2 − 12 h k + 9 k 2

361 x 2 − 121 361 x 2 − 121

p 3 + 216 p 3 + 216

8 x 3 − 125 8 x 3 − 125

64 q 3 − 27 p 3 64 q 3 − 27 p 3

4 x ( x − 1 ) − 1 4 + 3 ( x − 1 ) 3 4 4 x ( x − 1 ) − 1 4 + 3 ( x − 1 ) 3 4

3 p ( p + 3 ) 1 3 −8 ( p + 3 ) 4 3 3 p ( p + 3 ) 1 3 −8 ( p + 3 ) 4 3

4 r ( 2 r − 1 ) − 2 3 − 5 ( 2 r − 1 ) 1 3 4 r ( 2 r − 1 ) − 2 3 − 5 ( 2 r − 1 ) 1 3

Rational Expressions

For the following exercises, simplify the expression.

x 2 − x − 12 x 2 − 8 x + 16 x 2 − x − 12 x 2 − 8 x + 16

4 y 2 − 25 4 y 2 − 20 y + 25 4 y 2 − 25 4 y 2 − 20 y + 25

2 a 2 − a − 3 2 a 2 − 6 a − 8 ⋅ 5 a 2 − 19 a − 4 10 a 2 − 13 a − 3 2 a 2 − a − 3 2 a 2 − 6 a − 8 ⋅ 5 a 2 − 19 a − 4 10 a 2 − 13 a − 3

d − 4 d 2 − 9 ⋅ d − 3 d 2 − 16 d − 4 d 2 − 9 ⋅ d − 3 d 2 − 16

m 2 + 5 m + 6 2 m 2 − 5 m − 3 ÷ 2 m 2 + 3 m − 9 4 m 2 − 4 m − 3 m 2 + 5 m + 6 2 m 2 − 5 m − 3 ÷ 2 m 2 + 3 m − 9 4 m 2 − 4 m − 3

4 d 2 − 7 d − 2 6 d 2 − 17 d + 10 ÷ 8 d 2 + 6 d + 1 6 d 2 + 7 d − 10 4 d 2 − 7 d − 2 6 d 2 − 17 d + 10 ÷ 8 d 2 + 6 d + 1 6 d 2 + 7 d − 10

10 x + 6 y 10 x + 6 y

12 a 2 + 2 a + 1 − 3 a 2 −1 12 a 2 + 2 a + 1 − 3 a 2 −1

1 d + 2 c 6 c + 12 d d c 1 d + 2 c 6 c + 12 d d c

3 x − 7 y 2 x 3 x − 7 y 2 x

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