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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises

Review Exercises

Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

494.

y 2 + 8 y 20 y 2 + 8 y 20

495.

−6 a 4 −6 a 4

496.

9 x 3 1 9 x 3 1

497.

n 3 3 n 2 + 3 n 1 n 3 3 n 2 + 3 n 1

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

498.

16 x 2 40 x 25 16 x 2 40 x 25

499.

5 m + 9 5 m + 9

500.

−15 −15

501.

y 2 + 6 y 3 + 9 y 4 y 2 + 6 y 3 + 9 y 4

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

502.

4 p + 11 p 4 p + 11 p

503.

−8 y 3 5 y 3 −8 y 3 5 y 3

504.

Add 4n5,n5,−6n54n5,n5,−6n5

505.

Subtract 10x210x2 from 3x23x2

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

506.

( 4 a 2 + 9 a 11 ) + ( 6 a 2 5 a + 10 ) ( 4 a 2 + 9 a 11 ) + ( 6 a 2 5 a + 10 )

507.

( 8 m 2 + 12 m 5 ) ( 2 m 2 7 m 1 ) ( 8 m 2 + 12 m 5 ) ( 2 m 2 7 m 1 )

508.

( y 2 3 y + 12 ) + ( 5 y 2 9 ) ( y 2 3 y + 12 ) + ( 5 y 2 9 )

509.

( 5 u 2 + 8 u ) ( 4 u 7 ) ( 5 u 2 + 8 u ) ( 4 u 7 )

510.

Find the sum of 8q3278q327 and q2+6q2q2+6q2

511.

Find the difference of x2+6x+8x2+6x+8 and x28x+15x28x+15

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

512.

200x15x2200x15x2 when x=5x=5

513.

200x15x2200x15x2 when x=0x=0

514.

200x15x2200x15x2 when x=15x=15

515.

5+40x12x25+40x12x2 when x=10x=10

516.

5+40x12x25+40x12x2 when x=−4x=−4

517.

5+40x12x25+40x12x2 when x=0x=0

518.

A pair of glasses is dropped off a bridge 640640 feet above a river. The polynomial −16t2+640−16t2+640 gives the height of the glasses tt seconds after they were dropped. Find the height of the glasses when t=6.t=6.

519.

The fuel efficiency (in miles per gallon) of a bus going at a speed of xx miles per hour is given by the polynomial 1160x2+12x.1160x2+12x. Find the fuel efficiency when x=20x=20 mph.

Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

520.

6 3 6 3

521.

( 1 2 ) 4 ( 1 2 ) 4

522.

( −0.5 ) 2 ( −0.5 ) 2

523.

3 2 3 2

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

524.

p 3 · p 10 p 3 · p 10

525.

2 · 2 6 2 · 2 6

526.

a · a 2 · a 3 a · a 2 · a 3

527.

x · x 8 x · x 8

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

528.

( y 4 ) 3 ( y 4 ) 3

529.

( r 3 ) 2 ( r 3 ) 2

530.

( 3 2 ) 5 ( 3 2 ) 5

531.

( a 10 ) y ( a 10 ) y

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

532.

( 8 n ) 2 ( 8 n ) 2

533.

( −5 x ) 3 ( −5 x ) 3

534.

( 2 a b ) 8 ( 2 a b ) 8

535.

( −10 m n p ) 4 ( −10 m n p ) 4

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

536.

( 3 a 5 ) 3 ( 3 a 5 ) 3

537.

( 4 y ) 2 ( 8 y ) ( 4 y ) 2 ( 8 y )

538.

( x 3 ) 5 ( x 2 ) 3 ( x 3 ) 5 ( x 2 ) 3

539.

( 5 s t 2 ) 3 ( 2 s 3 t 4 ) 2 ( 5 s t 2 ) 3 ( 2 s 3 t 4 ) 2

Multiply Monomials

In the following exercises, multiply the monomials.

540.

( −6 p 4 ) ( 9 p ) ( −6 p 4 ) ( 9 p )

541.

( 1 3 c 2 ) ( 30 c 8 ) ( 1 3 c 2 ) ( 30 c 8 )

542.

( 8 x 2 y 5 ) ( 7 x y 6 ) ( 8 x 2 y 5 ) ( 7 x y 6 )

543.

( 2 3 m 3 n 6 ) ( 1 6 m 4 n 4 ) ( 2 3 m 3 n 6 ) ( 1 6 m 4 n 4 )

Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

544.

7 ( 10 x ) 7 ( 10 x )

545.

a 2 ( a 2 9 a 36 ) a 2 ( a 2 9 a 36 )

546.

−5 y ( 125 y 3 1 ) −5 y ( 125 y 3 1 )

547.

( 4 n 5 ) ( 2 n 3 ) ( 4 n 5 ) ( 2 n 3 )

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

548.

( a + 5 ) ( a + 2 ) ( a + 5 ) ( a + 2 )

549.

( y 4 ) ( y + 12 ) ( y 4 ) ( y + 12 )

550.

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

551.

( 6 p 11 ) ( 3 p 10 ) ( 6 p 11 ) ( 3 p 10 )

552.

( n + 8 ) ( n + 1 ) ( n + 8 ) ( n + 1 )

553.

( k + 6 ) ( k 9 ) ( k + 6 ) ( k 9 )

554.

( 5 u 3 ) ( u + 8 ) ( 5 u 3 ) ( u + 8 )

555.

( 2 y 9 ) ( 5 y 7 ) ( 2 y 9 ) ( 5 y 7 )

556.

( p + 4 ) ( p + 7 ) ( p + 4 ) ( p + 7 )

557.

( x 8 ) ( x + 9 ) ( x 8 ) ( x + 9 )

558.

( 3 c + 1 ) ( 9 c 4 ) ( 3 c + 1 ) ( 9 c 4 )

559.

( 10 a 1 ) ( 3 a 3 ) ( 10 a 1 ) ( 3 a 3 )

Multiply a Trinomial by a Binomial

In the following exercises, multiply using any method.

560.

( x + 1 ) ( x 2 3 x 21 ) ( x + 1 ) ( x 2 3 x 21 )

561.

( 5 b 2 ) ( 3 b 2 + b 9 ) ( 5 b 2 ) ( 3 b 2 + b 9 )

562.

( m + 6 ) ( m 2 7 m 30 ) ( m + 6 ) ( m 2 7 m 30 )

563.

( 4 y 1 ) ( 6 y 2 12 y + 5 ) ( 4 y 1 ) ( 6 y 2 12 y + 5 )

Divide Monomials

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

564.

2 8 2 2 2 8 2 2

565.

a 6 a a 6 a

566.

n 3 n 12 n 3 n 12

567.

x x 5 x x 5

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

568.

3 0 3 0

569.

y 0 y 0

570.

( 14 t ) 0 ( 14 t ) 0

571.

12 a 0 15 b 0 12 a 0 15 b 0

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

572.

( 3 5 ) 2 ( 3 5 ) 2

573.

( x 2 ) 5 ( x 2 ) 5

574.

( 5 m n ) 3 ( 5 m n ) 3

575.

( s 10 t ) 2 ( s 10 t ) 2

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

576.

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

577.

u 3 u 2 · u 4 u 3 u 2 · u 4

578.

( x x 9 ) 5 ( x x 9 ) 5

579.

( p 4 · p 5 p 3 ) 2 ( p 4 · p 5 p 3 ) 2

580.

( n 5 ) 3 ( n 2 ) 8 ( n 5 ) 3 ( n 2 ) 8

581.

( 5 s 2 4 t ) 3 ( 5 s 2 4 t ) 3

Divide Monomials

In the following exercises, divide the monomials.

582.

72 p 12 ÷ 8 p 3 72 p 12 ÷ 8 p 3

583.

−26 a 8 ÷ ( 2 a 2 ) −26 a 8 ÷ ( 2 a 2 )

584.

45 y 6 −15 y 10 45 y 6 −15 y 10

585.

−30 x 8 −36 x 9 −30 x 8 −36 x 9

586.

28 a 9 b 7 a 4 b 3 28 a 9 b 7 a 4 b 3

587.

11 u 6 v 3 55 u 2 v 8 11 u 6 v 3 55 u 2 v 8

588.

( 5 m 9 n 3 ) ( 8 m 3 n 2 ) ( 10 m n 4 ) ( m 2 n 5 ) ( 5 m 9 n 3 ) ( 8 m 3 n 2 ) ( 10 m n 4 ) ( m 2 n 5 )

589.

42 r 2 s 4 6 r s 3 54 r s 2 9 s 42 r 2 s 4 6 r s 3 54 r s 2 9 s

Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

590.

6 −2 6 −2

591.

( −10 ) −3 ( −10 ) −3

592.

5 · 2 −4 5 · 2 −4

593.

( 8 n ) −1 ( 8 n ) −1

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

594.

x −3 · x 9 x −3 · x 9

595.

r −5 · r −4 r −5 · r −4

596.

( u v −3 ) ( u −4 v −2 ) ( u v −3 ) ( u −4 v −2 )

597.

( m 5 ) −1 ( m 5 ) −1

598.

( k −2 ) −3 ( k −2 ) −3

599.

q 4 q 20 q 4 q 20

600.

b 8 b −2 b 8 b −2

601.

n −3 n −5 n −3 n −5

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

602.

5,300,000 5,300,000

603.

0.00814 0.00814

604.

The thickness of a piece of paper is about 0.0970.097 millimeter.

605.

According to www.cleanair.com, U.S. businesses use about 21,000,00021,000,000 tons of paper per year.

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

606.

2.9 × 10 4 2.9 × 10 4

607.

1.5 × 10 8 1.5 × 10 8

608.

3.75 × 10 −1 3.75 × 10 −1

609.

9.413 × 10 −5 9.413 × 10 −5

Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

610.

( 3 × 10 7 ) ( 2 × 10 −4 ) ( 3 × 10 7 ) ( 2 × 10 −4 )

611.

( 1.5 × 10 −3 ) ( 4.8 × 10 −1 ) ( 1.5 × 10 −3 ) ( 4.8 × 10 −1 )

612.

6 × 10 9 2 × 10 −1 6 × 10 9 2 × 10 −1

613.

9 × 10 −3 1 × 10 −6 9 × 10 −3 1 × 10 −6

Introduction to Factoring Polynomials

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

614.

5 n , 45 5 n , 45

615.

8 a , 72 8 a , 72

616.

12 x 2 , 20 x 3 , 36 x 4 12 x 2 , 20 x 3 , 36 x 4

617.

9 y 4 , 21 y 5 , 15 y 6 9 y 4 , 21 y 5 , 15 y 6

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

618.

16 u 24 16 u 24

619.

15 r + 35 15 r + 35

620.

6 p 2 + 6 p 6 p 2 + 6 p

621.

10 c 2 10 c 10 c 2 10 c

622.

−9 a 5 9 a 3 −9 a 5 9 a 3

623.

−7 x 8 28 x 3 −7 x 8 28 x 3

624.

5 y 2 55 y + 45 5 y 2 55 y + 45

625.

2 q 5 16 q 3 + 30 q 2 2 q 5 16 q 3 + 30 q 2

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