Prealgebra 2e

# Review Exercises

Prealgebra 2eReview Exercises

### Review Exercises

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.

$y2+8y−20y2+8y−20$

495.

$−6a4−6a4$

496.

$9x3−19x3−1$

497.

$n3−3n2+3n−1n3−3n2+3n−1$

Determine the Degree of Polynomials

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

498.

$16x2−40x−2516x2−40x−25$

499.

$5m+95m+9$

500.

$−15−15$

501.

$y2+6y3+9y4y2+6y3+9y4$

In the following exercises, add or subtract the monomials.

502.

$4p+11p4p+11p$

503.

$−8y3−5y3−8y3−5y3$

504.

Add $4n5,−n5,−6n54n5,−n5,−6n5$

505.

Subtract $10x210x2$ from $3x23x2$

In the following exercises, add or subtract the polynomials.

506.

$(4a2+9a−11)+(6a2−5a+10)(4a2+9a−11)+(6a2−5a+10)$

507.

$(8m2+12m−5)−(2m2−7m−1)(8m2+12m−5)−(2m2−7m−1)$

508.

$(y2−3y+12)+(5y2−9)(y2−3y+12)+(5y2−9)$

509.

$(5u2+8u)−(4u−7)(5u2+8u)−(4u−7)$

510.

Find the sum of $8q3−278q3−27$ and $q2+6q−2q2+6q−2$

511.

Find the difference of $x2+6x+8x2+6x+8$ and $x2−8x+15x2−8x+15$

Evaluate a Polynomial for a Given Value of the Variable

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

512.

$200x−15x2200x−15x2$ when $x=5x=5$

513.

$200x−15x2200x−15x2$ when $x=0x=0$

514.

$200x−15x2200x−15x2$ when $x=15x=15$

515.

$5+40x−12x25+40x−12x2$ when $x=10x=10$

516.

$5+40x−12x25+40x−12x2$ when $x=−4x=−4$

517.

$5+40x−12x25+40x−12x2$ 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.

$6363$

521.

$(12)4(12)4$

522.

$(−0.5)2(−0.5)2$

523.

$−32−32$

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

524.

$p3·p10p3·p10$

525.

$2·262·26$

526.

$a·a2·a3a·a2·a3$

527.

$x·x8x·x8$

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

528.

$(y4)3(y4)3$

529.

$(r3)2(r3)2$

530.

$(32)5(32)5$

531.

$(a10)y(a10)y$

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

532.

$(8n)2(8n)2$

533.

$(−5x)3(−5x)3$

534.

$(2ab)8(2ab)8$

535.

$(−10mnp)4(−10mnp)4$

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

536.

$(3a5)3(3a5)3$

537.

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

538.

$(x3)5(x2)3(x3)5(x2)3$

539.

$(5st2)3(2s3t4)2(5st2)3(2s3t4)2$

Multiply Monomials

In the following exercises, multiply the monomials.

540.

$(−6p4)(9p)(−6p4)(9p)$

541.

$(13c2)(30c8)(13c2)(30c8)$

542.

$(8x2y5)(7xy6)(8x2y5)(7xy6)$

543.

$(23m3n6)(16m4n4)(23m3n6)(16m4n4)$

##### Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

544.

$7(10−x)7(10−x)$

545.

$a2(a2−9a−36)a2(a2−9a−36)$

546.

$−5y(125y3−1)−5y(125y3−1)$

547.

$(4n−5)(2n3)(4n−5)(2n3)$

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.

$(3x+1)(2x−7)(3x+1)(2x−7)$

551.

$(6p−11)(3p−10)(6p−11)(3p−10)$

552.

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

553.

$(k+6)(k−9)(k+6)(k−9)$

554.

$(5u−3)(u+8)(5u−3)(u+8)$

555.

$(2y−9)(5y−7)(2y−9)(5y−7)$

556.

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

557.

$(x−8)(x+9)(x−8)(x+9)$

558.

$(3c+1)(9c−4)(3c+1)(9c−4)$

559.

$(10a−1)(3a−3)(10a−1)(3a−3)$

Multiply a Trinomial by a Binomial

In the following exercises, multiply using any method.

560.

$(x+1)(x2−3x−21)(x+1)(x2−3x−21)$

561.

$(5b−2)(3b2+b−9)(5b−2)(3b2+b−9)$

562.

$(m+6)(m2−7m−30)(m+6)(m2−7m−30)$

563.

$(4y−1)(6y2−12y+5)(4y−1)(6y2−12y+5)$

##### Divide Monomials

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

564.

$28222822$

565.

$a6aa6a$

566.

$n3n12n3n12$

567.

$xx5xx5$

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

568.

$3030$

569.

$y0y0$

570.

$(14t)0(14t)0$

571.

$12a0−15b012a0−15b0$

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

572.

$(35)2(35)2$

573.

$(x2)5(x2)5$

574.

$(5mn)3(5mn)3$

575.

$(s10t)2(s10t)2$

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

576.

$(a3)2a4(a3)2a4$

577.

$u3u2·u4u3u2·u4$

578.

$(xx9)5(xx9)5$

579.

$(p4·p5p3)2(p4·p5p3)2$

580.

$(n5)3(n2)8(n5)3(n2)8$

581.

$(5s24t)3(5s24t)3$

Divide Monomials

In the following exercises, divide the monomials.

582.

$72p12÷8p372p12÷8p3$

583.

$−26a8÷(2a2)−26a8÷(2a2)$

584.

$45y6−15y1045y6−15y10$

585.

$−30x8−36x9−30x8−36x9$

586.

$28a9b7a4b328a9b7a4b3$

587.

$11u6v355u2v811u6v355u2v8$

588.

$(5m9n3)(8m3n2)(10mn4)(m2n5)(5m9n3)(8m3n2)(10mn4)(m2n5)$

589.

$42r2s46rs3−54rs29s42r2s46rs3−54rs29s$

##### Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

590.

$6−26−2$

591.

$(−10)−3(−10)−3$

592.

$5·2−45·2−4$

593.

$(8n)−1(8n)−1$

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

594.

$x−3·x9x−3·x9$

595.

$r−5·r−4r−5·r−4$

596.

$(uv−3)(u−4v−2)(uv−3)(u−4v−2)$

597.

$(m5)−1(m5)−1$

598.

$(k−2)−3(k−2)−3$

599.

$q4q20q4q20$

600.

$b8b−2b8b−2$

601.

$n−3n−5n−3n−5$

Convert from Decimal Notation to Scientific Notation

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

602.

$5,300,0005,300,000$

603.

$0.008140.00814$

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.

$2.9×1042.9×104$

607.

$1.5×1081.5×108$

608.

$3.75×10−13.75×10−1$

609.

$9.413×10−59.413×10−5$

Multiply and Divide Using Scientific Notation

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

610.

$(3×107)(2×10−4)(3×107)(2×10−4)$

611.

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

612.

$6×1092×10−16×1092×10−1$

613.

$9×10−31×10−69×10−31×10−6$

##### Introduction to Factoring Polynomials

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

614.

$5n,455n,45$

615.

$8a,728a,72$

616.

$12x2,20x3,36x412x2,20x3,36x4$

617.

$9y4,21y5,15y69y4,21y5,15y6$

Factor the Greatest Common Factor from a Polynomial

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

618.

$16u−2416u−24$

619.

$15r+3515r+35$

620.

$6p2+6p6p2+6p$

621.

$10c2−10c10c2−10c$

622.

$−9a5−9a3−9a5−9a3$

623.

$−7x8−28x3−7x8−28x3$

624.

$5y2−55y+455y2−55y+45$

625.

$2q5−16q3+30q22q5−16q3+30q2$