Part I -- EXPONENTS, ADD/SUBTRACT POLYNOMIALS, AND MULTIPLYING MONOMIALS

Name: Date: Algebra I – 3rd Quarterly Test

Part I -- EXPONENTS, ADD/SUBTRACT POLYNOMIALS, AND

MULTIPLYING MONOMIALS

1.) −6x3n+1y, where n is an integer. (A) The expression is a monomial (B) The expression is a binomial (C) The expression is a trinomial (D) The expression is not a polynomial (E) None of the above

2.) 2xx 2

(A) The expression is a monomial (B) The expression is a binomial (C) The expression is a trinomial (D) The expression is not a polynomial (E) None of the above

3.) 3x−2x2+5x

(A) The expression is a monomial (B) The expression is a binomial (C) The expression is a trinomial (D) The expression is not a polynomial (E) None of the above

4.) 5x yz 2 10

(A) The expression is a 0th degree polynomial (B) The expression is a 10th degree polynomial (C) The expression is a 11th degree polynomial (D) The expression is a 12th degree polynomial (E) The expression is a 13th degree polynomial

Name: Date: 5.) 25x y2 3−10y5−25y x3 23

(A) The expression is a 0th degree polynomial (B) The expression is a 10th degree polynomial (C) The expression is a 11th degree polynomial (D) The expression is a 12th degree polynomial (E) The expression is a 13th degree polynomial

6.) Simplify

(

)

(

)

4 4 6 3 2 2 2 4 3 4 4 4 5 4 − ÷ ÷ ⋅ − (A) 35 2 (B) 175 36 (C) 35 6 (D) 75 26 (E) 165 136 7.) Simplify 2x−4y− +x 3y (A) y−x (B) 3x−y (C) x−7y (D) (− −y x) (E) (x −y) 8.) Simplify 2 2 3 2 3 2 2x 8x y 2x 4xy x 2x y − + − + + − (A) 3 2 2 2 2 6 4 x x x y xy − − + + (B) −3x3+10x y2 (C) −3x3+10xy2 (D) 3 2 2 2 10 x x x y − − + (E) −3x5+10x y3 3

Name: Date: 9.) Simplify ( 2− − + + − − − +a 3b 5) ( a 5b 3) (A) a+2b−2 (B) a−2b−8 (C) 3a+2b−8 (D) 3a−2b+2 (E) 3− +a 2b+8 10.) Simplify 2 2 3 2 2 ( 4x y 2xy 3y ) (3x y 5y 2xy ) − − − + − − − (A) 2 2 3 4x y+xy +5y−3y (B) 5xy2+2y3 (C) 5xy2+2y4 (D) 2 2 3 4 5 3 x y+ xy + y− y (E) 2 3 5xy +5y−3y 11.) Solve 6x− − − =( 3x 1) 10 (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 12.) Solve (3y2−2y+10) 3(− y2−2y+ =8) 10 (A) 3 (B) 4 (C) 5 (D) 6 (E) 7

Name: Date: 13.) Simplifyx x⋅ 7 (A) x 23 (B) 7 x (C) x 9 (D) x−8 (E) 7 x− 14.) Simplify 3 2 (xy )(x y ) (A) x y 2 4 (B) 4 3 x y (C) x y 3 4 (D) x y 2 3 (E) 4 4 x y 15.) Simplify(−x4)(−x)3 (A) −x7 (B) 12 x (C) −x12 (D) 2x− (E) x 7 16.) Simplify 3 2 3 5 (4x zy )(6zy x ) (A) 8 2 5 10x z y (B) 10x z y 8 2 7 (C) 24x zy 3 5 (D) 8 2 5 24x z y (E) 15 2 5 10x z y

Name: Date: 17.) Simplify

(

( )

3

)

(

( ) ( )

2 3

)

( )

( )

2 3 r s r s s − − − − (A) −3r s3 5 (B) 9r s 4 6 (C) 3 6 9r s − (D) −6r s4 6 (E) 4 5 6r s 18.) Simplify 4 3 5 4 5x 2x          (A) 50x 12 (B) 12 2x (C) 50x 7 (D) 20x 12 (E) 7 2x 19.) Simplify 24

( ) ( )

3 1

( )

3 4 x y 6 x y − −     − − −         (A) 4 5 y x − (B) x3y4 (C) −36x3y4 (D) 4 4 x y − (E) 3 5 y x − 20.) Simplify 2⋅22n ⋅52n ⋅5= (A) 10⋅72n (B) 4n 10 10⋅ (C) 10⋅102n2 (D) 2 1 10 n+ (E) 4n 10

Name: Date:

Part II -- POWER OF MONOMIALS, DIVIDING MONOMIALS,

NEGATIVE EXPONENTS AND EXPONENTIAL EQUATIONS

Simplify Each Expression

21.) 3 5 (x ) = (A) 15 y (B) x14⋅x (C) 3x 5 (D) 3 5x (E) x−15 22.) 2 3 (−z ) = (A) z−1 (B) 6 z (C) 6 z − (D) z−6 (E) −z5 23.) 3 2 5 ( ( (− − −x ) )) = (A) 11 x (B) −x13 (C) x 10 (D) 10 x − (E) x 30

Name: Date: 24.) 3 4 2 (3r s ) =________ (A) 9s r 6 8 (B) 8 6 9s r (C) 6 5 6s r (D) 9s r 6 5 (E) 8 6 6s r 25.) 2 3 1 (2 ) 2y y   =     (A) 5 2 y (B) 2 y (C) 5 4 y (D) 6 8 y (E) 6 y 5 26.) 0 1 2 3 (((2 ) ) ) (A) 0 (B) 64 (C) 12 (D) 1 (E) 8 27.) 2 3 3 2 (2x ) +(3 )x = (A) 17x 12 (B) 6 17x (C) 72x 12 (D) 12x 10 (E) 12 12x

Name: Date: 28.) 2 3 3 2 (2x ) (3 )x = (A) 17x 12 (B) 6 17x (C) 12 72x (D) 12x 10 (E) 12 12x 29.) 3 2 2 5 2 2 (( ) ) (2 ( ) ) p −p q +p p −q = (A) 5 p q 7 4 (B) −4 p q7 4 (C) 14 8 2 p q − (D) 14 8 5 p q (E) −4 p q14 8 30.) 3 2 2 5 2 2 (( ) ) (2 ( ) ) p −p q ⋅p p −q = (A) 7 4 3 p q (B) 7 4 4 p q − (C) −2 p q14 8 (D) 14 8 5 p q (E) 14 8 4 p q 31.) 3 ( )n x = (A) x3 n+ (B) 3 n x (C) x 3n (D)

( )

3x n (E)

( )

xn 3

Name: Date: 32.) x x x x = (A) 2 x x (B) x 2 x (C) x x2 (D) 2 2x x (E)

( )

2x x 33.) x x2 x3 a a a = (A) ax x+ +2 x3 (B) 6 x a (C) x6 a (D) 6a x (E) 3x3 a 34.) (ax) (x bx x) = (A)

( )

ab 4 x (B) a2x⋅b2x (C)

( )

2 x ab (D) a4x⋅b4x (E)

( )

2 4 x ab 35.) 2 2 (3 ) (4rn q )n = (A) 9 4⋅

( )

rq 2n (B) 9 2⋅

( )

rq 2n (C) 9 4⋅ nr q2n n (D) 9 4⋅ nr qn 2n (E) 2 2 12 n n r q ⋅

Name: Date: 36.) 2 2 (2xn) n+(4x n n) = (A) 22nx 4n (B) 4nx2n2 (C) 2 4 2 nx n (D) 8nx2n2 (E) 22n+1x2n2

Divide, and write the result as a fraction. Assume that no denominator equals 0.

37.) 119 51 = (A) 39 17 (B) 17 7 (C) 7 3 (D) 17 3 (E) 39 7 38.) 12345 12344 90 90 = (A) 1 901234 (B) 901234 (C) 1 90 (D) 90 (E) 1

Name: Date: 39.) 33 333 3 3 = (A) 300 3 (B) ₃₀₀1 3 (C) 111 1111 (D) 1 27 (E) 1 9 40.) 91 117 t E n A f l Y t i g E r S ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (A) 7 9 n A f l y i g r s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (B) 7 9 n A f L Y i g r s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (C) 7 9 N A f l Y i g r s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (D) 7 9 n A f l Y I g r s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (E) 7 9 n A f l Y i g r S ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

Name: Date: 41.) 10 7 25 5 w w = (A) 3 5w (B) 5w 17 (C) 5w−3 (D) 3 5 w (E) 20w 3 42.) 4 2 2 6x y x y = (A) 2 x y (B) 6x y 2 2 (C) 6x y 2 (D) 4 2 6x y (E) 2 2 x y 43.) 2 2 2 6 xy x y = (A) 6 y x (B) 3 y x (C) 1 3xy (D) 3xy (E) 3x y 2 2

Name: Date: 44.) 3 3 4 2 35 5 ab c a b c = (A) 2 4 7bc a (B) 32 4 7bc a (C) 3 2 3 7b c a (D) 2 3 7 bc a ⋅ (E) 3 3 7bc a

Find the value of each expression. Give your answers using integers or fractions

45.) −3−3 = (A) 1 27 (B) 1 27 − (C) 9 (D) 27 (E) 27− 46.) ( 2)− −4 = (A) 16 (B) 8− (C) 1 16 (D) 6−

Name: Date: 47.) ( 1)− −3⋅ −( 2)−4 = (A) 16 (B) 8 (C) 1 16 (D) 14− (E) 1 16 − 48.) (( 2) )− −1 2 = (A) 4− (B) 4 (C) 1 4 − (D) 1 4 (E) 2− 49.) 1₃ 4− = − (A) 64− (B) 12 (C) 1 12 − (D) 1 12 (E) 12−

Name: Date: 50.) 3 32⋅ −5 = (A) 27− (B) 36 (C) 1 36 − (D) 1 27 (E) 9− 51.) 3 4 6 6 − − = (A) 6− (B) 6 (C) 1 6 − (D) 1 6 (E) 6 7 52.) 3 2 2 3 3 −   =     (A) 1 (B) 12 3 (C) 1₁₂ 3 (D) 1 36 (E) 3 7

Name: Date: 53.) (4−1⋅3 )− −1 1 = (A) 7 (B) 1 12 − (C) 12− (D) 12 (E) 1 7 54.) 2 3 4 −   =     (A) 9 16 (B) 16 9 (C) 4 3 (D) 3 4 (E) 6 8 − − 55.) 2 1 0 2 2 3 4 − − −  _⋅  =     (A) 8 3 (B) 1 8 (C) 8 (D) 64− (E) 1 64

Name: Date: 56.)

(

1

)

3 2 3⋅ − − = (A) 27 8 (B) 1 8 (C) 9 4 (D) 2 3 (E) 18−

Simplify. Give your answers using positive exponents.

57.) 2x−3 = (A) 6x− (B) 8 x (C) 2₃ x (D) 5x− (E) x− 58.) 2 (3 )x − = (A) 6x− (B) 6 x (C) 2 x (D) 1₂ 9x (E) x

Name: Date: 59.) 2 2 3 2d c − −   =     (A) 4 6 4d c (B) 6 4 4c d (C) 4 6 4 d c (D) 6 4 4 c d (E) 5 4 4c d 60.) (a a2 −3 3) = (A) 3 a (B) 1₃ a (C) 3a− (D) 1 3a (E) 1 3a −

Name: Date: 61.) 3 2 3 2 3 2 4 2 x y z x y z − − − − = (A) 6 5 2x yz (B) 5 5 2x z y (C) 4 5 2x yz (D) 4 5 2x y z (E) 5 5 2x y z

Solve each equation.

62.) 2 2 2 x+ =1 (A) 3− (B) 2− (C) 1− (D) 0 (E) 1 63.) 32 3− x =3−2x (A) 1− (B) 0 (C) 1 (D) 2 (E) 3

Name: Date: 64.) 33m⋅3−2m = ⋅3 3−2m (A) 1 3 (B) 2 5 (C) 1 2 (D) 2 (E) 3− 65.) 1 5 5 5 5 x x x x + − − = (A) 3 1 (B) 4 1 − (C) 2 1 (D) −4 (E) 2 66.) 3 1 81 9 x⋅ = (A) 3 (B) 4 (C) 5 (D) 6 (E) 7

Name: Date: 67.) 81 3⋅ −2x =93x−2 (A) 1− (B) 0 (C) 1 (D) 2 (E) 3 68.) 2 5 64 4 128 n n + − = (A) 13 2 − (B) 3 2 (C) 2 1 (D) 13 10 (E) −2 69.) 2 1 3 1 1 9 3 27 x x +   ⋅ =     (A) 13 2 − (B) 3 2 (C) 2 1 (D) 13 10 (E) 2 1 −

Name: Date: 70.) 25x =8x−1, what is the value of x ?

(A) 4 1 (B) 2 3 − (C) 2 1 (D) 8 1 (E) 2 1 −

71.) If m and k are positive and 3 2

2m k− =100m, what is 2 m− in terms of k ? (A) 10 k (B) 10 k (C) ₂ 50 1 k (D) 100₂ k (E) 50k 2 72.) If xy=30 and =15 y z

, what is the value of xz ? (A) 2 (B) 15 (C) 2 1 (D) 450 (E) 45

Name: Date:

73.) If a , b , and c are different positive integers and 22⋅ ⋅ ⋅ =2a 2b 2c 256, then

1 1 1 2a+ +2b+ +2c+ =? (A) 192 (B) 512 (C) 8 (D) 6 (E) 28 74.) If 30 6 x m m m = and 15 4 y m m m   =  

  , what is the value of x−y?

(A) 31 (B) 41 (C) 55 (D) 17 (E) 5

75.) If 3 92⋅ +x 32x+2+9x+1=38, what is the value of x ?

(A) 2 11 (B) 4 3 (C) 2 5 (D) 3 1 (E) 2 1

76.) If x=3yand y=z−1, what is 3x in term of z ? (A) 3 z

(B) z3 (C) 3

z

Name: Date:

Part III -- FACTORING POLYNOMIALS

Factor each expression completely

77.) c d3 −c d4 3 = (A) c3d(−cd2) (B) c3d(1−cd) (C) 3(1 2) cd c − (D) c3d(1−d2) (E) c3d(1−cd2) 78.) 3 x + =x (A) x(x+1)(x+1) (B) x(x2 +1) (C) (x+1)(x2 +1) (D) 4 2x (E) 2( +1) x x 79.) 3 2 4 4 x ₋x ₌ (A)

(

)

4 1 − x (B) 4 3x2 (C) 4 ) 1 )( 1 (x+ x− x (D)

(

1

)

4 2 − x x (E) 4x2

(

x−1

)

Name: Date: 80.) xx+4−xx+5 = (A) x (B) −x (C) xx+4(1−x) (D) − 2x+9 x (E) xx2+9x+20 81.) 3 2 3 2 2 3 a b c+ab c +a bc = (A) abc a b b c( 2 + 2 +ac2) (B) ab(a2b2 +b2c+ac2) (C) 2 2 2 2 ( ) abc a b +b c+ac (D) ( 2 2 2 2) c c b b a abc + + (E) abc(a2b2 +bc+ac2) 82.) z2 −9= (A) (x+3)(x−3) (B) 2 ) 3 (z− (C) (z+3)2 (D) (z+9)(z−9) (E) (z+3)(z−3) 83.) p2−q2 = (A) 2 ) (p+q (B) (p+q)(p−q) (C) 2 2 q p − (D) 2 ) (p−q (E) p2 +q2

Name: Date: 84.) 49x2−36= (A) (7x−36)(7x+36) (B) (49x−6)(49x+6) (C) (6x−7)(6x+7) (D) (7x−6)(7x+6) (E) (49x−36)(49x+36) 85.) 36 2 1 49x − = (A) 2 1 7 6       − x (B) 2 1 7 6       + x (C) (6 7)(6 7) 49 1 _{+ −} x x (D) (6x+7)(6x−7) (E) (6 7)(6 7) 36 1 _{+ −} x x 86.) (x+y)2−x2 = (A) (2x+y)y (B) y 2 (C) 2x+y (D) 2x−y2 (E) x3y2 87.) 2 1 (− +x 1) = (A) x2 +1 (B) −x (C) −x2 (D) −x(x+2) (E) x 2

Name: Date: 88.) x2−2x−80= (A) (x−8)(x+10) (B) (x+8)(x−10) (C) (x+20)(x−4) (D) (x−20)(x+4) (E) (x+40)(x−2) 89.) 10x2−9x+ =2 (A) (2x+1)(5x−2) (B) (5x−1)(2x−2) (C) (2x−1)(5x−2) (D) (5x−1)(2x+2) (E) (2x−1)(5x+2) 90.) 2 2 13x −5xy−8y = (A) (7x+8y)(6x− y) (B) (13x−4y)(x+2y) (C) (13x−y)(x+8y) (D) (13x+8y)(x−y) (E) (13x+2y)(x−4y) 91.) 2 2 6 ab+a b − = (A) (a−2b)(a+3b) (B) (ab−2)(ab+3) (C) (a+2b)(a−3b) (D) Prime (E) (a−6b)(a+b)

Name: Date: 92.) 15x2n+4+22xn+2+ =8 (A) (3 n+2 +2)(5 n+2 +4) x x (B) (3xn+4 +2)(5x2n +4) (C) (5xn+4 +2)(3x2n +4) (D) (3 n+2 +4)(5 n+2 +2) x x (E) (xn+2 +2)(15xn+2 +4) 93.) 3(c+d)2+10(c+ + =d) 8 (A) (3c+d +4)(c+3d +2) (B) (3c+3d +1)(c+d+8) (C) (c+d +4)(3c+3d +2) (D) (3c+d+4)(3c+d +2) (E) (3c+3d +4)(c+d +2) 94.) 3 2 3 3 9 x + x + x+ = (A) (x2 +3)2 (B) x(x2 +3) (C) (x+3)(x2 +3) (D) ( +9)( 2 +3) x x (E) (x+3)(x2 +9) 95.) a b+ +xa+xb= (A) x(a+b) (B) (a+1)(x+b) (C) (a+x)(b+1) (D) (a+b)(x+1) (E) x(a+b+1)

Name: Date: 96.) y2−6y+ −9 9z2 = (A) (y+3z)(y−6−3z) (B) (y−3+3z)(y−3−3z) (C) (y−3z)(y−3−9z) (D) (y+3+3z)(y−3+3z) (E) (y−3+3z)(y+3−3z) 97.) 9x2 −9y2 +6y−1= (A) (3x−3y+1)(3x+3y−1) (B) (3x−y+3)(3x+3y−1) (C) (9x−3y−1)(x+3y+1) (D) (3x−3y+1)(3x+ y−3) (E) (x−3y+1)(9x+3y−1) 98.) 6x y2 −11x y2 2−10x y2 3= (A) 2(3 2 2)(2 5 ) y y y x + − (B) x2y(2+2y)(3−5y) (C) (3x2 +2y)(2x−5y2) (D) y(3x+2y)(2x−5y) (E) x2y(3+2y)(2−5y) 99.) 2 2 81c −9d = (A) (9c+3d)(9c−d) (B) (9c+d)(9c−d) (C) 9(3c+d)(3c−d) (D) 9(c−d)(3c+d) (E) 9(3c d c− )( +3 )d

Name: Date: 100.) 3x5−108x+15x3 = (A) (3 2 +9)( +2)( −2) x x x x (B) 3(x3 +9)(x2 +4) (C) 3x(x2 +9)(x2 +4) (D) 3 ( 2 +9)( +2)( −2) x x x x (E) 3x(x2 +4)(x+3)(x−3) 101.) x8− =1 (A) (x4 −1)(x2 +1)(x+1)(x−1) (B) (x4 +1)(x2 +1)(x+1)(x−1) (C) (x4 +1)(x2 +1)(x2 −1) (D) ( 4 −1)( 4 +1) x x (E) (x4 +1)(x2 +1)(x−1)(x−1) 102.) 4 2 2x y+8y−10x y= (A) 2(x+1)(x−1)(x+2)(x−2) (B) 2( 2 + )( 2 +4) x y y x (C) 2y((x2 +1)(x2 +4) (D) 2y(x4 −5x2 −4) (E) 2 (y x+1)(x−1)(x+2)(x−2) 103.) p4−80p q2 2−81q4 = (A) (p2 +q2)(p+9q)(p−9q) (B) (p2 +q2)(p2 +81q2) (C) (p+q)(p−q)(p+9q)(p−9q) (D) (p2 +q2)(p+9q)2 (E) (p2 −q2)(p+9q)(p−9q)

Name: Date: 104.) (x+1)4− −(x 1)4 = (A) ( +1)( −1)( 2 +1)( 4 +1) x x x x (B) 8x(x2 +1) (C) 8x2(x+1)(x−1) (D) 4(x2 +1)(x2 −1) (E) 2( 2 +1) x x 105.) c3+2c2+ =9 (A) (c+3)(c2 −3) (B) c2(c−3) (C) ( +3)( 2 − +3) c c c (D) Prime (E) c(c2 −2c+9) 106.) 4 4 4 x + y = (A) (x2 +4y2)(x2+y2) (B) (x2 +2y2)2 (C) ( 2 2 2)( 2 2 2) y x y x + − (D) Prime (E) (x2 +2xy+2y2)(x2 −2xy+2y2) 107.) (x+1)(x+2)(x+3)(x+ + =4) 1 (A) x(x+5)(x+1)(x+2) (B) (x+5x+5)2 (C) (x+5x+5)(x+1) (D) Prime (E) (x+5)(x+1)(x+2)(x+3)

Name: Date:

Answers:

1.) A 2.) D 3.) B 4.) E 5.) C 6.) B 7.) D 8.) A 9.) C 10.) D 11.) B 12.) D 13.) A 14.) C 15.) E 16.) D 17.) B 18.) E 19.) D 20.) D 21.) B 22.) C 23.) E 24.) B 25.) A 26.) D 27.) B 28.) C 29.) A 30.) E 31.) C 32.) B 33.) A 34.) C 35.) B 36.) E 37.) C 38.) D 39.) B 40.) E 41.) A 42.) C 43.) B 44.) D 45.) A 46.) C 47.) E 48.) D 49.) A 50.) D 51.) B 52.) C 53.) D 54.) B 55.) E 56.) A 57.) C 58.) D 59.) C 60.) B 61.) E 62.) C 63.) D 64.) A 65.) B 66.) D 67.) C 68.) A 69.) E 70.) B 71.) C 72.) D 73.) E 74.) B 75.) C 76.) A 77.) E 78.) B 79.) D 80.) C 81.) A 82.) E 83.) B 84.) D 85.) C 86.) A 87.) D 88.) B 89.) C 90.) D 91.) B 92.) A 93.) E 94.) C 95.) D 96.) B 97.) A 98.) E 99.) C 100.) D 101.) B 102.) E 103.) A 104.) B 105.) C 106.) E 107.) B

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